Hüseyin Budak

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Generalized Ostrowski type inequalities for local fractional integrals

2016-12-07

First, we establish the generalized Ostrowski inequality for local fractional integrals on fractal sets<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript alpha"><mml:semantics><mml:msup><mml:mi>R</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>α</mml:mi></mml:mrow></mml:msup><mml:annotation encoding="application/x-tex">R^{\alpha }</mml:annotation></mml:semantics></mml:math></inline-formula><inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 0 greater-than alpha less-than-or-equal-to … First, we establish the generalized Ostrowski inequality for local fractional integrals on fractal sets<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript alpha"><mml:semantics><mml:msup><mml:mi>R</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>α</mml:mi></mml:mrow></mml:msup><mml:annotation encoding="application/x-tex">R^{\alpha }</mml:annotation></mml:semantics></mml:math></inline-formula><inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 0 greater-than alpha less-than-or-equal-to 1 right-parenthesis"><mml:semantics><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>></mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">\left ( 0>\alpha \leq 1\right )</mml:annotation></mml:semantics></mml:math></inline-formula>of real line numbers. Secondly, we obtain some new inequalities using the generalized convex function on fractal sets<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript alpha"><mml:semantics><mml:msup><mml:mi>R</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>α</mml:mi></mml:mrow></mml:msup><mml:annotation encoding="application/x-tex">R^{\alpha }</mml:annotation></mml:semantics></mml:math></inline-formula>.

Fractional Hermite-Hadamard-type inequalities for interval-valued functions

2019-08-07

Hüseyin Budak , Tuba Tunç , Mehmet Zeki Sarıkaya

In this paper, we define interval-valued right-sided Riemann- Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals. In this paper, we define interval-valued right-sided Riemann- Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals.

Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions

2020-07-29

Hüseyin Budak , Muhammad Aamir Ali , Meliha Tarhanaci

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

2020-07-19

Hüseyin Budak , Samet Erden , Muhammad Aamir Ali

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some … We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

2021-01-21

Muhammad Aamir Ali , Mujahid Abbas , Hüseyin Budak +3 more

Abstract In this research, we derive two generalized integral identities involving the $q^{\varkappa _{2}}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:msub><mml:mi>ϰ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:msup></mml:math> -quantum integrals and quantum numbers, the results are then used to establish some new … Abstract In this research, we derive two generalized integral identities involving the $q^{\varkappa _{2}}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:msub><mml:mi>ϰ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:msup></mml:math> -quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q -differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit $q\rightarrow 1^{-}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mo>−</mml:mo></mml:msup></mml:math> in the key results of this paper.

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Some new Simpson's type inequalities for coordinated convex functions in quantum calculus

2020-12-01

Muhammad Aamir Ali , Hüseyin Budak , Zhiyue Zhang +1 more

In this article, by using the notion of newly defined q 1 q 2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes … In this article, by using the notion of newly defined q 1 q 2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes raised in this paper are extensions and generalizations of the comparable results in the literature on Simpson's inequalities for coordinated convex functions.

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives

2021-01-06

Muhammad Aamir Ali , Hüseyin Budak , Mujahid Abbas +1 more

Abstract In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:mi>b</mml:mi></mml:msup></mml:math> -integral. We prove some new inequalities related with right-hand sides of … Abstract In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:mi>b</mml:mi></mml:msup></mml:math> -integral. We prove some new inequalities related with right-hand sides of $q^{b}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:mi>b</mml:mi></mml:msup></mml:math> -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

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Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

2021-01-01

Muhammad Aamir Ali , Hüseyin Budak , Abdullah Akkurt +1 more

Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">∣</m:mo> <m:mrow> <m:mmultiscripts> <m:mrow> <m:mi>D</m:mi> </m:mrow> … Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">∣</m:mo> <m:mrow> <m:mmultiscripts> <m:mrow> <m:mi>D</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> <m:mprescripts /> <m:none /> <m:mrow> <m:mi>b</m:mi> </m:mrow> </m:mmultiscripts> <m:mspace width="0.08em" /> <m:mi>f</m:mi> </m:mrow> <m:mo stretchy="false">∣</m:mo> </m:mrow> </m:math> | {}^{b}D_{q}^{2}\hspace{0.08em}f| and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">∣</m:mo> <m:mrow> <m:mmultiscripts> <m:mrow> <m:mi>D</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> <m:mprescripts /> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:none /> </m:mmultiscripts> <m:mspace width="0.08em" /> <m:mi>f</m:mi> </m:mrow> <m:mo stretchy="false">∣</m:mo> </m:mrow> </m:math> | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {q}_{a} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>b</m:mi> </m:mrow> </m:msup> </m:math> {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.

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New version of fractional Simpson type inequalities for twice differentiable functions

2021-10-18

Fatih Hezenci , Hüseyin Budak , Hasan Kara

Abstract Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. … Abstract Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.

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Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables

2021-01-07

Muhammad Aamir Ali , Yu–Ming Chu , Hüseyin Budak +3 more

Abstract In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for … Abstract In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of two variables via quantum integrals. We also consider the particular cases of the key results and offer some new integral inequalities.

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Some trapezoid and midpoint type inequalities for newly defined quantum integrals

2021-01-16

Hüseyin Budak

In this paper, we first obtain prove two new identities for the quantum integrals. Then we establish Trapezoid and Midpoint type inequalities for quantum integrals defined by Bermudo et al. … In this paper, we first obtain prove two new identities for the quantum integrals. Then we establish Trapezoid and Midpoint type inequalities for quantum integrals defined by Bermudo et al. in [3]. The inequalities in this study generalize some results obtained in earlier works

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On generalized some integral inequalities for local fractional integrals

2016-01-07

Mehmet Zeki Sarıkaya , Tuba Tunç , Hüseyin Budak

On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals

2021-05-27

Hüseyin Budak , Fatih Hezenci , Hasan Kara

The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities … The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities for the functions whose derivatives in absolute value are convex. Finally, we show that our main inequalities reduce to Ostrowski type inequalities, Simpson type inequalities and trapezoid type inequalities which are proved in earlier published papers.

Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions

2022-03-21

Thanin Sitthiwirattham , Kamsing Nonlaopon , Muhammad Aamir Ali +1 more

In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newton’s type … In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newton’s type for functions of bounded variation. It is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. Finally, we give some examples with graphs and show the validity of newly established inequalities.

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Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

2020-07-14

Hasan Kara , Muhammad Aamir Ali , Hüseyin Budak

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals. In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.

On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions

2021-01-01

Muhammad Aamir Ali , Necmettin Alp , Hüseyin Budak +2 more

Abstract The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. The consequences derived in this paper are unification and generalization of the comparable … Abstract The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. The consequences derived in this paper are unification and generalization of the comparable consequences in the literature on midpoint inequalities.

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Generalized Hermite-Hadamard type integral inequalities for fractional integrals

2016-01-01

Mehmet Sarikay , Hüseyin Budak

In this paper, we have established Hermite-Hadamard type inequalities for fractional integrals depending on a parameter. In this paper, we have established Hermite-Hadamard type inequalities for fractional integrals depending on a parameter.

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New inequalities of Opial type for conformable fractional integrals

2017-01-01

Mehmet Zeki Sarıkaya , Hüseyin Budak

Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

2021-06-29

Miguel Vivas–Cortez , Muhammad Aamir Ali , Hüseyin Budak +2 more

In this investigation, for convex functions, some new (p,q)–Hermite–Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates … In this investigation, for convex functions, some new (p,q)–Hermite–Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

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Quantum Ostrowski‐type integral inequalities for functions of two variables

2021-02-08

Hüseyin Budak , Muhammad Aamir Ali , Tuba Tunç

In this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed … In this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed that the results presented in this paper are the consolidation and generalization of some existing results on the literature of Ostrowski inequalities.

Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020-09-18

Dafang Zhao , Muhammad Aamir Ali , Artion Kashuri +2 more

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h -convex functions”. We establish some inequalities … Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h -convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

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On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

2021-06-26

Hüseyin Budak , Fatih Hezenci , Hasan Kara

Abstract In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some … Abstract In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

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Ostrowski and Simpson type inequalities for multiplicative integrals

2021-05-18

Muhammad Aamir Ali , Hüseyin Budak , Mehmet Zeki Sarıkaya +1 more

In this paper, we firstly obtain two identities for multiplicative differentiable functions. Then by using these identities, we establish Ostrowski and Simpson type inequalities for multiplicative integrals. At the end … In this paper, we firstly obtain two identities for multiplicative differentiable functions. Then by using these identities, we establish Ostrowski and Simpson type inequalities for multiplicative integrals. At the end we give detail applications of our main results

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Refinements of quantum Hermite-Hadamard-type inequalities

2021-01-01

Hüseyin Budak , Sundas Khan , Muhammad Aamir Ali +1 more

Abstract In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities. Abstract In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.

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Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method

2018-09-01

Samad Noeiaghdam , Muhammad Suleman , Hüseyin Budak

The susceptible–infected–recovered model of computer viruses is investigated as a nonlinear system of ordinary differential equations by using the homotopy analysis method (HAM). The HAM is a flexible method which … The susceptible–infected–recovered model of computer viruses is investigated as a nonlinear system of ordinary differential equations by using the homotopy analysis method (HAM). The HAM is a flexible method which contains the auxiliary parameters and functions. This method has an important tool to adjust and control the convergence region of obtained solution. The numerical solutions are presented for various iterations, and the residual error functions are applied to show the accuracy of presented method. Several $$\hbar$$ -curves are plotted to demonstrate the regions of convergence, and the residual errors are obtained for different values of theses regions.

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Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions

2021-01-01

Hüseyin Budak , Hasan Kara , Muhammad Aamir Ali +2 more

Abstract In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued … Abstract In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by applying the newly defined fractional integrals. The results of the present paper are the extension of several previously published results.

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On new Milne-type inequalities for fractional integrals

2023-01-18

Hüseyin Budak , Pınar Kösem , Hasan Kara

Abstract In this study, fractional versions of Milne-type inequalities are investigated for differentiable convex functions. We present Milne-type inequalities for bounded functions, Lipschitz functions, functions of bounded variation, etc., found … Abstract In this study, fractional versions of Milne-type inequalities are investigated for differentiable convex functions. We present Milne-type inequalities for bounded functions, Lipschitz functions, functions of bounded variation, etc., found in the literature. New results are established in the area of inequalities. This article is the first to study Milne-type inequalities for fractional integrals.

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On Hermite-Hadamard type inequalities for multiplicative fractional integrals

2020-01-01

Hüseyin Budak , Kubilay Özçelik

In this study, we first establish two Hermite-Hadamard type inequality for multiplicative (geometric) Riemann-Liouville fractional integrals.Then, by using some properties of multiplicative convex function, we give some new inequalities involving … In this study, we first establish two Hermite-Hadamard type inequality for multiplicative (geometric) Riemann-Liouville fractional integrals.Then, by using some properties of multiplicative convex function, we give some new inequalities involving multiplicative fractional integrals.

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A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021-04-29

Yi-Xia Li , Muhammad Aamir Ali , Hüseyin Budak +2 more

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented … Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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New Inequalities for Local Fractional Integrals

2017-10-27

Hüseyin Budak , Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

Generalized fractional integral inequalities of Hermite–Hadamard type for harmonically convex functions

2020-03-26

Dafang Zhao , Muhammad Aamir Ali , Artion Kashuri +1 more

Abstract In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained … Abstract In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite–Hadamard type.

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On new inequalities of Simpson's type for generalized convex functions

2019-06-30

Mehmet Zeki Sarıkaya , Hüseyin Budak , Samet Erden

In this paper, using local fractional integrals on fractal sets $R^{\alpha }$ $\left( 0<\alpha \leq 1\right) $ of real line numbers, we establish new some inequalities of Simpson's type based … In this paper, using local fractional integrals on fractal sets $R^{\alpha }$ $\left( 0<\alpha \leq 1\right) $ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

Weighted Hermite–Hadamard type inclusions for products of co-ordinated convex interval-valued functions

2021-02-10

Hasan Kara , Hüseyin Budak , Muhammad Aamir Ali +2 more

Abstract In this paper, we establish some Hermite–Hadamard–Fejér type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works. Abstract In this paper, we establish some Hermite–Hadamard–Fejér type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works.

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On the Hadamard’s type inequalities for co-ordinated convex functions via fractional integrals

2016-06-24

Abdullah Akkurt , Mehmet Zeki Sarıkaya , Hüseyin Budak +1 more

In this paper, we establish two identities for functions of two variables and apply them to give new Hermite–Hadamard type fractional integral inequalities for double fractional integrals involving functions whose … In this paper, we establish two identities for functions of two variables and apply them to give new Hermite–Hadamard type fractional integral inequalities for double fractional integrals involving functions whose derivatives are bounded or co-ordinates convex function on Δ≔[a,b]×[c,d] in R2 with a<b,c<d.

Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

2016-12-01

Hüseyin Budak , Mehmet Zeki Sarıkaya , Erhan Set

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

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Hermite-Hadamard's inequalities for conformable fractional integrals

2019-01-31

Mehmet Zeki Sarıkaya , Abdullah Akkurt , Hüseyin Budak +2 more

In this paper, we establish the Hermite-Hadamard type inequalities forconformable fractional integral and we will investigate some integralinequalities connected with the left and right-hand side of theHermite-Hadamard type inequalities for … In this paper, we establish the Hermite-Hadamard type inequalities forconformable fractional integral and we will investigate some integralinequalities connected with the left and right-hand side of theHermite-Hadamard type inequalities for conformable fractional integral. Theresults presented here would provide generalizations of those given inearlier works and we show that some of our results are better than the otherresults with respect to midpoint inequalities.

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On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators

2018-01-01

Fuat Usta , Hüseyin Budak , Mehmet Zeki Sarıkaya +1 more

By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite-Hadamard?s type inequality and conclude explicit bounds for the trapezoid inequalities … By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite-Hadamard?s type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where |f'| and |f''| (or |f'|q and |f''|q for q ? 1) are s-convex hold by applying the H?lder inequality and the power mean inequality.

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Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions

2021-01-01

Miguel Vivas–Cortez , Muhammad Aamir Ali , Artion Kashuri +1 more

<abstract> In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of … <abstract> In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, $ k $-Riemann-Liouville ($ k $-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel. </abstract>

Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

2021-11-25

Muhammad Aamir Ali , Hasan Kara , Jessada Tariboon +3 more

From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. … From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

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Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals

2016-08-30

Abdullah Akkurt , Mehmet Zeki Sarıkaya , Hüseyin Budak +1 more

Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

2021-04-29

Muhammad Aamir Ali , Hüseyin Budak , Ghulam Murtaza +1 more

Abstract In this research, we introduce the notions of $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities … Abstract In this research, we introduce the notions of $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

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Generalized p-Convex Fuzzy-Interval-Valued Functions and Inequalities Based upon the Fuzzy-Order Relation

2022-01-26

Muhammad Bilal Khan , Savin Treanţă , Hüseyin Budak

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the … Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p,s)-convex fuzzy interval-valued functions ((p,s)-convex F-I-V-Fs) in the second sense and to establish Hermite–Hadamard (H–H) type inequalities for (p,s)-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for (p,s)-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

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A companion of Ostrowski type inequalities for mappings of bounded variation and some applications

2017-04-14

Hüseyin Budak , Mehmet Zeki Sarıkaya

In this paper, we establish a companion of Ostrowski type inequalities for mappings of bounded variation and the quadrature formula is also provided. In this paper, we establish a companion of Ostrowski type inequalities for mappings of bounded variation and the quadrature formula is also provided.

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

2021-06-07

Xuexiao You , Muhammad Aamir Ali , Hüseyin Budak +2 more

Abstract In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for … Abstract In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

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New Simpson type inequalities for twice differentiable functions via generalized fractional integrals

2021-12-11

Xuexiao You , Fatih Hezenci , Hüseyin Budak +1 more

<abstract>Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity … <abstract>Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity for twice differentiable functions. Furthermore, by utilizing generalized fractional integrals, we prove several Simpson type inequalities for functions whose second derivatives in absolute value are convex.</abstract>

A NEW VERSION OF NEWTON’S INEQUALITIES FOR RIEMANN–LIOUVILLE FRACTIONAL INTEGRALS

2023-02-01

Fatih Hezenci , Hüseyin Budak , Pınar Kösem

We establish some Newton's type inequalities in the case of differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Furthermore, we give an example with graph and present the validity … We establish some Newton's type inequalities in the case of differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Furthermore, we give an example with graph and present the validity of the newly obtained inequalities. Finally, we give some inequalities of Riemann–Liouville fractional Newton's type for functions of bounded variation.

Some generalized Ostrowski type inequalities involving local fractional integrals and applications

2016-03-25

Mehmet Zeki Sarıkaya , Samet Erden , Hüseyin Budak

In this paper, we establish the generalized Ostrowski type inequality involving local fractional integrals on fractal sets Rα(0 < α ≤ 1) of real line numbers. Some applications for special … In this paper, we establish the generalized Ostrowski type inequality involving local fractional integrals on fractal sets Rα(0 < α ≤ 1) of real line numbers. Some applications for special means of fractal sets Rα are also given. The results presented here would provide extensions of those given in earlier works.

On Generalization of Dragomir’s Inequalities

2017-09-18

Hüseyin Budak , Mehmet Zeki Sarıkaya

In this paper, we establish some generalization of weighted Ostrowski type integral inequalities for functions of bounded variation. In this paper, we establish some generalization of weighted Ostrowski type integral inequalities for functions of bounded variation.

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New generalized midpoint type inequalities for fractional integral

2019-01-01

Hüseyin Budak , Praveen Agarwal

Here, our first aim to establish a new identity for differentiable function involving Riemann-Liouville fractional integrals.Then, we obtain same generalized midpoint type inequalities utilizing convex and concave function. Here, our first aim to establish a new identity for differentiable function involving Riemann-Liouville fractional integrals.Then, we obtain same generalized midpoint type inequalities utilizing convex and concave function.

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Simpson’s and Newton’s Type Inequalities for (α,m)-Convex Functions via Quantum Calculus

2022-04-03

Jarunee Soontharanon , Muhammad Aamir Ali , Hüseyin Budak +2 more

In this paper, we give the generalized version of the quantum Simpson’s and quantum Newton’s formula type inequalities via quantum differentiable α,m-convex functions. The main advantage of these new inequalities … In this paper, we give the generalized version of the quantum Simpson’s and quantum Newton’s formula type inequalities via quantum differentiable α,m-convex functions. The main advantage of these new inequalities is that they can be converted into quantum Simpson and quantum Newton for convex functions, Simpson’s type inequalities α,m-convex function, and Simpson’s type inequalities without proving each separately. These inequalities can be helpful in finding the error bounds of Simpson’s and Newton’s formulas in numerical integration. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.

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Comprehensive study of Weddle’s formula-type inequalities for convex functions within the framework of quantum calculus and their computational analysis

2025-05-26

Abdul Mateen , Hüseyin Budak , Artion Kashuri +1 more

Fractional Boole’s inequalities for twice differentiable functions for Riemann–Liouville fractional integrals

2025-04-11

Asia Shehzadi , Hüseyin Budak , Wali Haider +2 more

Hermite–Hadamard-Type Inequalities Arising from Tempered Fractional Integrals Including Twice-Differentiable Functions

2025-04-03

Fatih Hezenci , Hüseyin Budak , Muhammad Amer Latif

A Fractional Version of Corrected Dual-Simpson's Type Inequality via s−convex Function with Applications

2025-03-24

Arslan Munir , Ather Qayyum , Hüseyin Budak +3 more

Convexity plays a crucial role in mathematical analysis, offering profound insights into the behavior of functions and geometric shapes. Fractional integral operators generalize the classical concept of integration to non-integer … Convexity plays a crucial role in mathematical analysis, offering profound insights into the behavior of functions and geometric shapes. Fractional integral operators generalize the classical concept of integration to non-integer orders. In this paper, we establish a new identity by using the Caputo--Fabrizio fractional integral operator. Then by using this new identity, we obtain the corrected dual Simpson's type inequalities for s−convex functions. By employing the well-known integral inequalities such as the Hölder's inequality and power-mean inequality, we obtain new error estimates. Furthermore, we discuss the applications to some special means and quadrature formula.

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On the Fractional Inequalities of the Milne Type

2025-03-22

Hüseyin Budak , Hasan Kara , Hasan Öğünmez

ABSTRACT Our investigations in this paper revolve around exploring fractional variants of inequalities of Milne type by applying twice differentiable convex mappings. Based on some principles of convexity, Hölder inequality, … ABSTRACT Our investigations in this paper revolve around exploring fractional variants of inequalities of Milne type by applying twice differentiable convex mappings. Based on some principles of convexity, Hölder inequality, and power‐mean inequality, novel inequalities are derived. The acquired inequalities are supported by illustrative examples, which are calculated via their proofs. Additionally, graphical representations are to verify the examples visually. Furthermore, this investigation unveils fresh findings within the realm of inequalities.

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CORRECTED EULER-MACLAURIN-TYPE INEQUALITIES FOR ψ-HILFER FRACTIONAL INTEGRALS

2025-02-28

Umut Baş , Hüseyin Budak , Hüseyin Yıldırım +1 more

Abstract. In this article, novel Euler-Maclaurin type inequalities have been derived. These inequalities have been obtained through the use of ψ -Hilfer fractional integrals. In the process of deriving these … Abstract. In this article, novel Euler-Maclaurin type inequalities have been derived. These inequalities have been obtained through the use of ψ -Hilfer fractional integrals. In the process of deriving these inequalities, the condition that the absolute value of the derivative of the function f is convex has been taken into consideration. Furthermore, to facilitate the understanding of the main results presented in the article, special cases of the derived theorems have been examined, and various examples have been provided to illustrate these results concretely. Thus, the study also demonstrates how the obtained theoretical findings can be applied in a broader context.

On new versions of Milne-type inequalities based on Tempered fractional integrals

2025-02-28

Asia Shehzadi , Hüseyin Budak , Wali Haider +2 more

On multiplicative conformable fractional integrals: theory and applications

2025-02-27

Hüseyin Budak , Büşra Betül Ergün

A Study on Fractional Integral Inequalities for Trigonometric and Exponential Trigonometric-convex Functions

2025-02-14

Arslan Munir , Shumin Li , Hüseyin Budak +2 more

Inequalities involving fractional operators have also been an active area of research. These inequalities play a crucial role in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. … Inequalities involving fractional operators have also been an active area of research. These inequalities play a crucial role in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, firstly we establish these new identities for the case of twice differentiable functions and Caputo-Fabrizio fractional integrals. By utilizing these new identities, novel inequalities are obtained for trigonometric convex functions, and exponential trigonometric convex functions and exponential trigonometric convex functions. It is expected that the outcomes of this research will point to new developments in the study of fractional calculus.

New insights on fractal–fractional integral inequalities: Hermite–Hadamard and Milne estimates

2025-02-11

Abdelghani Lakhdari , Hüseyin Budak , Nabil Mlaiki +2 more

Novel Fractional Boole’s-Type Integral Inequalities via Caputo Fractional Operator and Their Implications in Numerical Analysis

2025-02-07

Wali Haider , Abdul Mateen , Hüseyin Budak +2 more

The advancement of fractional calculus, particularly through the Caputo fractional derivative, has enabled more accurate modeling of processes with memory and hereditary effects, driving significant interest in this field. Fractional … The advancement of fractional calculus, particularly through the Caputo fractional derivative, has enabled more accurate modeling of processes with memory and hereditary effects, driving significant interest in this field. Fractional calculus also extends the concept of classical derivatives and integrals to noninteger (fractional) orders. This generalization allows for more flexible and accurate modeling of complex phenomena that cannot be adequately described using integer-order derivatives. Motivated by its applications in various scientific disciplines, this paper establishes novel n-times fractional Boole’s-type inequalities using the Caputo fractional derivative. For this, a fractional integral identity is first established. Using the newly derived identity, several novel Boole’s-type inequalities are subsequently obtained. The proposed inequalities generalize the classical Boole’s formula to the fractional domain. Further extensions are presented for bounded functions, Lipschitzian functions, and functions of bounded variation, providing sharper bounds compared to their classical counterparts. To demonstrate the precision and applicability of the obtained results, graphical illustrations and numerical examples are provided. These contributions offer valuable insights for applications in numerical analysis, optimization, and the theory of fractional integral equations.

Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators

2025-02-04

Noureddine Azzouz , Bouharket Benaissa , Hüseyin Budak +1 more

Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions

2025-02-04

Areej A. Almoneef , Abd‐Allah Hyder , Fatih Hezenci +1 more

This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with … This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite–Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis.

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Novel generalized tempered fractional integral inequalities for convexity property and applications

2025-02-01

Artion Kashuri , Arslan Munir , Hüseyin Budak +1 more

OPEN NEWTON–COTES INEQUALITIES FOR CONVEX FUNCTIONS IN FRACTIONAL CALCULUS

2025-02-01

Thanin Sitthiwirattham , Muhammad Aamir Ali , Hüseyin Budak +1 more

Numerical Approximations and Fractional Calculus: Extending Boole’s Rule with Riemann–LiouvilleFractional Integral Inequalities

2025-01-18

Abdul Mateen , Wali Haider , Asia Shehzadi +2 more

This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integrals is … This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable convex functions. The proposed framework encompasses a wide range of functional classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation, thereby broadening the applicability of these inequalities to diverse mathematical settings. The research emphasizes the importance of the Riemann–Liouville fractional operator in solving problems related to non-integer-order differentiation, highlighting its pivotal role in enhancing classical inequalities. These newly established inequalities offer sharper error bounds for various numerical quadrature formulas in classical calculus, marking a significant advancement in computational mathematics. Numerical examples, computational analysis, applications to quadrature formulas and graphical illustrations substantiate the efficacy of the proposed inequalities in improving the accuracy of integral approximations, particularly within the context of fractional calculus. Future directions for this research include extending the framework to incorporate q-calculus, symmetrized q-calculus, alternative fractional operators, multiplicative calculus, and multidimensional spaces. These extensions would enable a comprehensive exploration of Boole’s formula and its associated error bounds, providing deeper insights into its performance across a broader range of mathematical and computational settings.

Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes

2025-01-14

Abdelghani Lakhdari , Muhammad Uzair Awan , Sever S Dragomir +2 more

Advancements in Hermite–Hadamard Inequalities via Conformable Fractional Integrals for Subadditive Functions

2025-01-09

Wali Haider , Hüseyin Budak , Asia Shehzadi +2 more

International Journal of Geometric Methods in Modern PhysicsAccepted Papers No AccessAdvancements in Hermite–Hadamard Inequalities via Conformable Fractional Integrals for Subadditive FunctionsWali Haider, Huseyin Budak, Asia Shehzadi, Fatih Hezenci, and Haibo … International Journal of Geometric Methods in Modern PhysicsAccepted Papers No AccessAdvancements in Hermite–Hadamard Inequalities via Conformable Fractional Integrals for Subadditive FunctionsWali Haider, Huseyin Budak, Asia Shehzadi, Fatih Hezenci, and Haibo ChenWali Haider, Huseyin Budak Search for more papers by this author , Asia Shehzadi Search for more papers by this author , Fatih Hezenci Search for more papers by this author , and Haibo Chenhttps://orcid.org/0000-0002-9868-7079 Search for more papers by this author https://doi.org/10.1142/S0219887825500999Cited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Cite Recommend Remember to check out the Most Cited Articles! Check out new Mathematical Physics books in our Mathematics 2021 catalogue Featuring authors Bang-Yen Chen, John Baez, Matilde Marcolli and more! We recommendImpact of a unilateral horizontal gene transfer on the evolutionary equilibria of a populationAlejandro Garriz, Mathematical Models and Methods in Applied Sciences, 2024Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable methodM. Shokrpour Roudbari, Mathematical Models and Methods in Applied Sciences, 2018Stochastic persistency of nematic alignment state for the Justh–Krishnaprasad model with additive white noisesSeung-Yeal Ha, Mathematical Models and Methods in Applied Sciences, 2020Asymptotic behavior and control of a "guidance by repulsion" modelDongnam Ko, Mathematical Models and Methods in Applied Sciences, 2020Uniform-in-time error estimate of the random batch method for the Cucker–Smale modelSeung-Yeal Ha, Mathematical Models and Methods in Applied Sciences, 2021An overview on the principle of inkjet printing technique and its application in micro-display for augmented/virtual realities by Compuscript Ltd, Opto-Electronic Advances, 2022Top-down control of bottom-up material synthesis @ nanoscale Saulius Juodkazis, Opto-Electronic Advances, 2023Advances in distributed fiber optic vibration/acoustic sensing technology Shuaiqi Liu, Opto-Electronic Advances, 2022Physics-data-driven intelligent optimization for large-aperture metalenses Yingli Ha, Opto-Electronic Advances, 2023Highly sensitive microfiber ultrasound sensor for photoacoustic imaging Perry Ping Shum, Opto-Electronic Advances, 2023Powered by Privacy policyGoogle Analytics settings FiguresReferencesRelatedDetails Recommended Accepted Papers Metrics History Received 8 August 2024 Accepted 13 December 2024 PDF download

Generalized local fractional integral inequalities via generalized (h̃1,h̃2)-preinvexity on fractal sets

2025-01-09

Sa’ud Al-Sa’di , Maria Bibi , Muhammad Muddassar +1 more

International Journal of Geometric Methods in Modern PhysicsAccepted Papers No AccessGeneralized local fractional integral inequalities via generalized (˜h1,˜h2)(h̃1,h̃2)-preinvexity on fractal setsSa'ud Al-Sadi, Maria Bibi, Muhammad Muddassar, and Huseyin BudakSa'ud Al-Sadi, … International Journal of Geometric Methods in Modern PhysicsAccepted Papers No AccessGeneralized local fractional integral inequalities via generalized (˜h1,˜h2)(h̃1,h̃2)-preinvexity on fractal setsSa'ud Al-Sadi, Maria Bibi, Muhammad Muddassar, and Huseyin BudakSa'ud Al-Sadi, Maria Bibi Search for more papers by this author , Muhammad Muddassar Search for more papers by this author , and Huseyin Budakhttps://orcid.org/0000-0001-8843-955X Search for more papers by this author https://doi.org/10.1142/S0219887825501002Cited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Cite Recommend Remember to check out the Most Cited Articles! Check out new Mathematical Physics books in our Mathematics 2021 catalogue Featuring authors Bang-Yen Chen, John Baez, Matilde Marcolli and more! We recommendGeneralized Invariant Sets for the Boltzmann EquationT. Goudon, Mathematical Models and Methods in Applied Sciences, 2011Fractional-Order Dual-Slope Integral Fast Analog-to-Digital Converter with High SensitivityBo Yu, Journal of Circuits, Systems and Computers, 2019Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional LaplacianJuan Pablo Borthagaray, Mathematical Models and Methods in Applied Sciences, 2019ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE SYSTEM OF HOPFIELD NEURAL NETWORKS VIA MATRIX INEQUALITIES AND APPLICATIONInternational Journal of Neural Systems, 2011Nonlinear Semi-Supervised Metric Learning Via Multiple Kernels and Local TopologyXin Li, International Journal of Neural Systems, 2018Liposomal Bupivacaine Analgesia in Deep Inferior Epigastric Perforator Flap Breast Reconstruction: A Retrospective Cohort Study .Liposomal bupivacaine for sleeve gastrectomy is associated with improved opioid outcomes and lower odds of opioid use disorder: claims-based analysis .Powered by Privacy policyGoogle Analytics settings FiguresReferencesRelatedDetailsNone Recommended Recommended SOME BULLEN-TYPE INEQUALITIES FOR GENERALIZED FRACTIONAL INTEGRALSDAFANG ZHAO, MUHAMMAD AAMIR ALI, HÜSEYIN BUDAK, and ZAI-YIN HEFractalsVol. 31, No. 04Several New Integral Inequalities via Caputo k-Fractional Derivative OperatorsSaad Ihsan Butt, M. Emin Özdemir, Muhammad Umar, and Bariş Çeli̇kAsian-European Journal of MathematicsVol. 14, No. 09GENERALIZED h-CONVEXITY ON FRACTAL SETS AND SOME GENERALIZED HADAMARD-TYPE INEQUALITIESWENBING SUNFractalsVol. 28, No. 02NEWTON'S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALSSabah Iftikhar, Poom Kumam, and Samet ErdenFractalsVol. 28, No. 03MILNE-TYPE FRACTAL INTEGRAL INEQUALITIES FOR GENERALIZED m-CONVEX MAPPINGSA'UD AL-SA'DI, MARIA BIBI, YOUNGSOO SEOL, and MUHAMMAD MUDDASSARFractalsVol. 31, No. 05CERTAIN INTEGRAL INEQUALITIES CONSIDERING GENERALIZED m-CONVEXITY ON FRACTAL SETS AND THEIR APPLICATIONSTINGSONG DU, HAO WANG, MUHAMMAD ADIL KHAN, and YAO ZHANGFractalsVol. 27, No. 07SOLUTION OF LOCAL FRACTIONAL GENERALIZED FOKKER–PLANCK EQUATION USING LOCAL FRACTIONAL MOHAND ADOMIAN DECOMPOSITION METHODSAAD ALTHOBAITI, RAVI SHANKER DUBEY, and JYOTI GEETESH PRASADFractalsVol. 30, No. 01NEW ESTIMATES OF INTEGRAL INEQUALITIES VIA GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTIONSAIMA RASHID, ZAKIA HAMMOUCH, FAHD JARAD, and YU-MING CHUFractalsVol. 28, No. 08 Accepted Papers Metrics Downloaded 0 times History Received 23 January 2024 Accepted 10 December 2024 PDF download

Advancements in corrected Euler–Maclaurin-type inequalities via conformable fractional integrals

2025-01-09

Yaren Acar , Hüseyin Budak , Umut Baş +2 more

Milne-type inequalities for third differentiable and h-convex functions

2025-01-07

Bouharket Benaissa , Hüseyin Budak

Some novel inequalities of Weddle’s formula type for Riemann–Liouville fractional integrals with their applications to numerical integration

2025-01-01

Abdul Mateen , Zhiyue Zhang , Hüseyin Budak +1 more

On some inequalities related to open Newton-Cotes formulas for differentiable convex functions with applications

2025-01-01

Ifra Bashir Sial , Mei Sun , Muhammad Aamir Ali +1 more

In this paper, first, we prove a novel integral identity involving a single time-differentiable function. Then, we prove some new inequalities associated with one of the open Newton-Cotes formulas for … In this paper, first, we prove a novel integral identity involving a single time-differentiable function. Then, we prove some new inequalities associated with one of the open Newton-Cotes formulas for differentiable convex functions. The newly established inequalities can be helpful in finding the error bounds of one of the open Newton-Cotes formulas. Finally, some applications of the inequalities are also presented in the context of open Newton-Cotes formulas.

Some bounds of Hermite–Hadamard-type inequalities based on conformable fractional integrals

2025-01-01

Hüseyin Budak , Umut Baş , Hasan Kara +1 more

In this research, we establish the above and below bounds via the left and right sides of Hermite–Hadamard-type inequalities including conformable fractional integrals with the aid of the mappings whose … In this research, we establish the above and below bounds via the left and right sides of Hermite–Hadamard-type inequalities including conformable fractional integrals with the aid of the mappings whose second derivatives are bounded. Instead of using the convexity condition in these obtained inequalities, we used condition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo class="MathClass-open" stretchy="false">(</mml:mo><mml:mi>a</mml:mi> <mml:mo class="MathClass-bin" stretchy="false">+</mml:mo> <mml:mi>b</mml:mi> <mml:mo class="MathClass-bin" stretchy="false">−</mml:mo> <mml:mi>t</mml:mi><mml:mo class="MathClass-close" stretchy="false">)</mml:mo> <mml:mo class="MathClass-bin" stretchy="false">−</mml:mo> <mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo class="MathClass-open" stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo class="MathClass-close" stretchy="false">)</mml:mo> <mml:mo class="MathClass-rel" stretchy="false">≥</mml:mo> <mml:mn>0</mml:mn><mml:mo class="MathClass-punc" stretchy="false">,</mml:mo></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>t</mml:mi> <mml:mo class="MathClass-rel" stretchy="false">∈</mml:mo> <mml:mrow><mml:mo fence="true" form="prefix"> [</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo class="MathClass-punc" stretchy="false">,</mml:mo> <mml:mfrac><mml:mrow><mml:mi>a</mml:mi><mml:mo class="MathClass-bin" stretchy="false">+</mml:mo><mml:mi>b</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac> </mml:mrow><mml:mo fence="true" form="postfix">]</mml:mo></mml:mrow></mml:mrow></mml:math>. We have presented examples of the inequalities acquired. We have given the graph showing the correctness of the presented examples.

On Error Bounds for Milne’s Formula in Conformable Fractional Operators

2024-11-29

Fatih Hezenci , Hüseyin Budak

New results on Bullen-type inequalities for coordinated convex functions obtained by using conformable fractional integrals

2024-11-29

Fatih Hezenci , Hasan Kara , Hüseyin Budak

UDC 517.9 Our aim is to investigate novel Bullen-type inequalities for coordinated convex mappings by employing conformable fractional integrals. Initially, an identity incorporating the conformable fractional integrals was established to … UDC 517.9 Our aim is to investigate novel Bullen-type inequalities for coordinated convex mappings by employing conformable fractional integrals. Initially, an identity incorporating the conformable fractional integrals was established to serve for this purpose. By using this identity, new inequalities аre derived expanding the scope of previously established results obtained with the help of Riemann–Liouville integrals by making specific choices of variable and applying the Hölder inequality and the power-mean inequality.

New versions of the Hermite–Hadamard inequality for $(\phi -h)$-integrals

2024-11-21

Saira Bano Akbar , Mujahid Abbas , Waqas Nazeer +1 more

In this paper, we prove some new versions of the Hermite–Hadamard inequality for $({\phi}-h)$ -integrals. For this aim, we use the tangent and secant lines at the same special points. … In this paper, we prove some new versions of the Hermite–Hadamard inequality for $({\phi}-h)$ -integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.

Symmetric midpoint type inequalities for (α, m)-Convex Functions with Applications

2024-11-15

Rashida Hussain , Ghazala Gulshan , Atiq Ur Rehman +1 more

New Inequalities of Bullen-type for Twice-Differentiable Functions via Conformable Fractional Integrals

2024-11-06

Fatih Hezenci , Hüseyin Budak

Fractional Milne-type inequalities for twice differentiable functions for Riemann–Liouville fractional integrals

2024-10-18

Wali Haider , Hüseyin Budak , Asia Shehzadi

Remarks on Inequalities with Parameter by Conformable Fractional Integrals

2024-10-07

Fatih Hezenci , Miguel Vivas–Cortez , Hüseyin Budak

We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established … We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite–Hadamard-, Simpson-, and Bullen-type inequalities which are proved in earlier published papers. More precisely, some inequalities are acquired by taking advantage of the convexity, the Hölder, and the power mean inequalities. Finally, examples are given to illustrate the investigated results.

Hermite–Hadamard-type inequalities arising from tempered fractional integrals including twice-differentiable functions

2024-09-30

Fatih Hezenci , Hüseyin Budak , Muhammad Amer Latif

UDC 517.5 We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable … UDC 517.5 We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.

Novel Ostrowski–Type Inequalities for Generalized Fractional Integrals and Diverse Function Classes

2024-09-13

Areej A. Almoneef , Abd‐Allah Hyder , Mohamed A. Barakat +1 more

In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in … In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for functions whose derivatives have convex absolute values. A new condition for bounded variation functions is examined, as well as expansions to bounded and Lipschitzian derivatives. Our comprehension is improved by comparison with current findings, and recommendations for future study areas are given.

Analysing Milne-type inequalities by using tempered fractional integrals

2024-08-14

Wali Haider , Hüseyin Budak , Asia Shehzadi +2 more

Extension of Milne-type inequalities to Katugampola fractional integrals

2024-08-13

Abdelghani Lakhdari , Hüseyin Budak , Muhammad Uzair Awan +1 more

This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral … This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.

Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities

2024-08-06

Saira Bano Akbar , Mujahid Abbas , Hüseyin Budak

Abstract The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called $$(\phi \,-\,h)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mspace/> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mi>h</mml:mi> … Abstract The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called $$(\phi \,-\,h)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mspace/> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mi>h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> integrals and $$(\phi \,-\,h)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mspace/> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mi>h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> derivatives, respectively. Then we investigate some implicit integral inequalities for $$(\phi \,-\,h)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mspace/> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mi>h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for q -integrals are deduced. The results presented herein are applicable to convex, m -convex, and $$\hbar $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ħ</mml:mi> </mml:math> -convex functions defined on the non-negative part of the real line.

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Some Classical Inequalities Associated with Generic Identity and Applications

2024-08-06

Muhammad Zakria Javed , Muhammad Uzair Awan , Bandar Bin‐Mohsin +2 more

In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper … In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski’s inequality, trapezoidal inequality, midpoint inequality, Simpson’s inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of γ and parameter ξ.

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New Quantum Estimates for Midpoint and Trapezoid Type Inequalities Through (α,m)-Convex Functions with Applications

2024-08-06

Gulshan Ghazala , Ali Muhammad Aamir , Hüseyin Budak +1 more

The main goal of current investigation is to present two new q-integral identities for midpoint and trapezoid type inequalities. Then using these identities, we develop several new quantum estimates for … The main goal of current investigation is to present two new q-integral identities for midpoint and trapezoid type inequalities. Then using these identities, we develop several new quantum estimates for midpoint and trapezoid type inequalities via (α, m)-convexity. Some special cases of these new inequalities can be turned into quantum midpoint and quantum trapezoid type inequalities for convex functions, classical midpoint and trapezoid type inequalities for convex functions without having to prove each one separately. Finally, we discuss how the special means can be used to address newly discovered inequalities. 2010 Mathematics Subject Classification. 26D10, 26D15, 26B25.

Fractional Newton‐type integral inequalities by means of various function classes

2024-08-04

Fatih Hezenci , Hüseyin Budak

The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, some fractional Newton‐type inequalities are established by using … The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, some fractional Newton‐type inequalities are established by using convex functions. In addition, several fractional Newton‐type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton‐type inequalities for Lipschitzian functions. Furthermore, several Newton‐type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.

On error bounds for Milne's formula in conformable fractional operators

2024-08-04

Fatih Hezenci , Hüseyin Budak

UDC 517.9 Milne's formula is a mathematical expression used to approximate the value of a definite integral. The formula is particularly useful for problems encountered in physics, engineering, and various … UDC 517.9 Milne's formula is a mathematical expression used to approximate the value of a definite integral. The formula is particularly useful for problems encountered in physics, engineering, and various other scientific disciplines. We establish an equality for conformable fractional integrals. With the help of this equality, we obtain error bounds for one of the open Newton–Cotes formulas, namely, Milne's formula for the case of differentiable convex functions within the framework of fractional and classical calculus. Furthermore, we provide our results by using special cases of the obtained theorems.

New Results on Simpson-Type Inequalities for Co-ordinated Convex Function by Generalized Conformable Integrals

2024-07-27

Fatih Hezenci , Hüseyin Budak

In this paper, firstly, we prove an identity involving generalized conformable integrals. By using this obtained identity, we establish several Simpson-type inequalities for differentiable co-ordinated convex function by means of … In this paper, firstly, we prove an identity involving generalized conformable integrals. By using this obtained identity, we establish several Simpson-type inequalities for differentiable co-ordinated convex function by means of generalized conformable fractional integrals. More precisely, some Simpson-type inequalities are obtained using the well-known Hölder and Power mean inequalities. Furthermore, we also consider some special cases which can be deduced from the main results.

Weighted Čebyšev- and Ostrowski-type inequalities on time scales

2024-07-27

Mehmet Zeki Sarıkaya , Hüseyin Budak

In this paper, we first obtain a new identity for time scales by using a weighted kernel. Then, by using this equality, we prove a weighted Čeby šev inequality. Moreover, … In this paper, we first obtain a new identity for time scales by using a weighted kernel. Then, by using this equality, we prove a weighted Čeby šev inequality. Moreover, we establish a weighted Ostrowski-type inequality by using a method which is different from among in the literature.

Further refinements and inequalities of Fejer's type via GA-convexity

2024-07-12

Muhammad Amer Latif , Hüseyin Budak , Artion Kashuri

In this study, we introduce some new mappings in connection with Hermite-Hadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain … In this study, we introduce some new mappings in connection with Hermite-Hadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.

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Quantum symmetric integral inequalities for convex functions

2024-07-09

Ammara Nosheen , Sana Ijaz , Khuram Ali Khan +2 more

In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite–Hadamard type inequalities. The function involved in these inequalities are convex functions. In order … In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite–Hadamard type inequalities. The function involved in these inequalities are convex functions. In order to reach the target, left and right quantum symmetric derivative and corresponding integral are used. Furthermore, the Hölder inequality is established in the frame work of left and right quantum symmetric integral. The new results refined the results about integral inequalities that exist in the literature.

Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals

2024-07-04

Areej A. Almoneef , Abd‐Allah Hyder , Hüseyin Budak

Some New Approaches to Fractional Euler–Maclaurin-Type Inequalities via Various Function Classes

2024-06-26

Mehmet Gümüş , Fatih Hezenci , Hüseyin Budak

This paper aims to examine an approach that studies many Euler–Maclaurin-type inequalities for various function classes applying Riemann–Liouville fractional integrals. Afterwards, our results are provided by using special cases of … This paper aims to examine an approach that studies many Euler–Maclaurin-type inequalities for various function classes applying Riemann–Liouville fractional integrals. Afterwards, our results are provided by using special cases of obtained theorems and examples. Moreover, several Euler–Maclaurin-type inequalities are presented for bounded functions by fractional integrals. Some fractional Euler–Maclaurin-type inequalities are established for Lipschitzian functions. Finally, several Euler–Maclaurin-type inequalities are constructed by fractional integrals of bounded variation.

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Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s -convex function

2024-06-20

Arslan Munir , Miguel Vivas–Cortez , Ather Qayyum +3 more

Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have … Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for s-convex function are obtained. By employing well-known inequalities such as Hölder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.

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Weighted fractional inequalities for new conditions on h-convex functions

2024-06-18

Bouharket Benaissa , Noureddine Azzouz , Hüseyin Budak

Abstract We use a new function class called B -function to establish a novel version of Hermite–Hadamard inequality for weighted ψ -Hilfer operators. Additionally, we prove two new identities involving … Abstract We use a new function class called B -function to establish a novel version of Hermite–Hadamard inequality for weighted ψ -Hilfer operators. Additionally, we prove two new identities involving weighted ψ -Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B -function, we derive several trapezoid- and midpoint-type inequalities for h -convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h .

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Fractional Euler-Maclaurin-type inequalities for various function classes

2024-05-29

Fatih Hezenci , Hüseyin Budak

Abstract This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of … Abstract This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation.

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New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals

2024-05-23

Mehmet Eyüp Ki̇ri̇ş , Miguel Vivas–Cortez , Tuğba Yalçın Uzun +2 more

Abstract In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results … Abstract In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals.

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Coauthor	Papers Together
Mehmet Zeki Sarıkaya	117
Muhammad Aamir Ali	99
Hasan Kara	57
Fatih Hezenci	54
Kamsing Nonlaopon	25
Thanin Sitthiwirattham	20
Artion Kashuri	18
Samet Erden	18
Hüseyin Yıldırım	17
Fuat Usta	17
Muhammad Uzair Awan	16
Yu–Ming Chu	15
Sotiris K. Ntouyas	14
Abd‐Allah Hyder	13
Tuba Tunç	13
Miguel Vivas–Cortez	12
Mujahid Abbas	11
Zhiyue Zhang	11
Muhammad Zakria Javed	11
Jessada Tariboon	10
Asia Shehzadi	9
Areej A. Almoneef	9
Bandar Bin‐Mohsin	9
Wali Haider	9
Arslan Munir	9
Ghazala Gulshan	9
Rashida Hussain	9
Praveen Agarwal	8
Abdullah Akkurt	8
Ifra Bashir Sial	8
Necmettin Alp	8
Xuexiao You	7
Fongchan Wannalookkhee	7
Saad Ihsan Butt	7
Bouharket Benaissa	7
Pınar Kösem	7
Humaira Kalsoom	7
Fatma Ertuğral	6
Ather Qayyum	6
Muhammad Aslam Noor	6
Haibo Chen	6
Waewta Luangboon	6
Shahid Qaisar	6
Umut Baş	6
Mohamed A. Barakat	6
Mehmet Eyüp Kırış	6
Dafang Zhao	6
Hatice Yaldız	5
Kubilay Özçelik	5
Asad Sadiq	5

Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities

2012-01-06

Mehmet Zeki Sarıkaya , Erhan Set , Hatice Yaldız +1 more

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Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula

1998-09-01

Sever S Dragomir , Ravi P. Agarwal

On q-Hermite–Hadamard inequalities for general convex functions

2020-02-14

Sergio Bermudo , Péter Kórus , Juan E. Nápoles Valdés

Quantum calculus on finite intervals and applications to impulsive difference equations

2013-11-07

Jessada Tariboon , Sotiris K. Ntouyas

In this paper we initiate the study of quantum calculus on finite intervals. We define the -derivative and -integral of a function and prove their basic properties. As an application, … In this paper we initiate the study of quantum calculus on finite intervals. We define the -derivative and -integral of a function and prove their basic properties. As an application, we prove existence and uniqueness results for initial value problems for first- and second-order impulsive -difference equations. MSC:26A33, 39A13, 34A37.

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q -Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions

2016-10-06

Necmettin Alp , Mehmet Zeki Sarıkaya , Mehmet Kunt +1 more

In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have … In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works.

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Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula

2003-02-17

U.S. Kirmaci

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

2020-07-19

Hüseyin Budak , Samet Erden , Muhammad Aamir Ali

Some quantum estimates for Hermite–Hadamard inequalities

2014-12-18

Muhammad Aslam Noor , Khalida Inayat Noor , Muhammad Uzair Awan

Convex Functions, Partial Orderings, and Statistical Applications

1992-01-01

Josip ‎Pečarić , Frank Proschan , Y. L. Tong

On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals

2017-01-01

Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

In this paper, we have established Hermite-Hadamard-type inequalities for fractional integrals and will be given an identity.With the help of this fractional-type integral identity, we give some integral inequalities connected … In this paper, we have established Hermite-Hadamard-type inequalities for fractional integrals and will be given an identity.With the help of this fractional-type integral identity, we give some integral inequalities connected with the left-side of Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals.

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Selected Topics on Hermite-Hadamard Inequalities and Applications

2003-03-01

Sever S Dragomir , Charles Pearce

The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications … The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this monograph we present the basic facts related to Hermite- Hadamard inequalities for convex functions and a large number of results for special means which can naturally be deduced. Hermite-Hadamard type inequalities for other concepts of convexities are also given. The properties of a number of functions and functionals or sequences of functions which can be associated in order to refine the result are pointed out. Recent references that are available online are mentioned as well.

Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions

2020-07-29

Hüseyin Budak , Muhammad Aamir Ali , Meliha Tarhanaci

�ber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert

1937-12-01

Alexander Ostrowski

On new inequalities of Simpson’s type for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>s</mml:mi></mml:math>-convex functions

2010-09-01

Mehmet Zeki Sarıkaya , Erhan Set , M. Emіn Özdemіr

Fractional Calculus: Integral and Differential Equations of Fractional Order

2008-01-01

Rudolf Gorenflo , Francesco Mainardi

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for … We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating these operators in a way accessible to applied scientists, avoiding unproductive generalities and excessive mathematical rigor. By applying this technique we shall derive the analytical solutions of the most simple linear integral and differential equations of fractional order. We show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix. The topics discussed here will be: (a) essentials of Riemann-Liouville fractional calculus with basic formulas of Laplace transforms, (b) Abel type integral equations of first and second kind, (c) relaxation and oscillation type differential equations of fractional order.

Some quantum integral inequalities via preinvex functions

2015-08-08

Muhammad Aslam Noor , Khalida Inayat Noor , Muhammad Uzair Awan

On Simpson's inequality and applications

2000-01-01

Sever S Dragomir , Ravi P. Agarwal , Pietro Cerone

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Quantum integral inequalities for convex functions

2015-01-01

Weerawat Sudsutad , Sotiris K. Ntouyas , Jessada Tariboon

In this paper we establish some new quantum integral inequalities for convex functions. In this paper we establish some new quantum integral inequalities for convex functions.

Integral inequalities in q-calculus

2004-01-01

Hillel Gauchman

Some new Simpson's type inequalities for coordinated convex functions in quantum calculus

2020-12-01

Muhammad Aamir Ali , Hüseyin Budak , Zhiyue Zhang +1 more

On the generalization of some integral inequalities and their applications

2011-06-04

Mehmet Zeki Sarıkaya , Nesip Aktan

Theory and Applications of Fractional Differential Equations

2006-01-01

Anatoly A. Kilbas , H. M. Srivastava , Juan J. Trujillo

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives

2021-01-06

Muhammad Aamir Ali , Hüseyin Budak , Mujahid Abbas +1 more

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Some New Newton’s Type Integral Inequalities for Co-Ordinated Convex Functions in Quantum Calculus

2020-09-08

Miguel Vivas–Cortez , Muhammad Aamir Ali , Artion Kashuri +2 more

Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is … Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by associating with them certain criteria of quantum calculus and the convexity of the functions of various variables. In this article, by using the concept of recently defined q1q2 -derivatives and integrals, some of Newton’s type inequalities for co-ordinated convex functions are revealed. We also employ the limits of q1,q2→1− in new results, and attain some new inequalities of Newton’s type for co-ordinated convex functions through ordinary integral. Finally, we provide a thorough application of the newly obtained key outcomes, these new consequences can be useful in the integral approximation study for symmetrical functions, or with some kind of symmetry.

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New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

2021-01-21

Muhammad Aamir Ali , Mujahid Abbas , Hüseyin Budak +3 more

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Some trapezoid and midpoint type inequalities for newly defined quantum integrals

2021-01-16

Hüseyin Budak

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ON THE HADAMARD’S INEQULALITY FOR CONVEX FUNCTIONS ON THE CO-ORDINATES IN A RECTANGLE FROM THE PLANE

2001-12-01

Sever S Dragomir

An inequality of Hadamard's type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given. An inequality of Hadamard's type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane and some applications are given.

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New version of fractional Simpson type inequalities for twice differentiable functions

2021-10-18

Fatih Hezenci , Hüseyin Budak , Hasan Kara

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NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS

2019-12-18

Sabah Iftikhar , Poom Kumam , Samet Erden

We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and … We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and their some powers are generalized convex are obtained. Some applications of these inequalities for Simpson’s quadrature rules and generalized special means are also given.

Quantum integral inequalities on finite intervals

2014-03-26

Jessada Tariboon , Sotiris K. Ntouyas

In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, Cauchy-Bunyakovsky-Schwarz, Grüss, and Grüss-Čebyšev integral inequalities. … In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, Cauchy-Bunyakovsky-Schwarz, Grüss, and Grüss-Čebyšev integral inequalities. The analysis relies on the notions of q-derivative and q-integral on finite intervals introduced by the authors in (Tariboon and Ntouyas in Adv. Differ. Equ. 2013:282, 2013). MSC: 34A08, 26D10, 26D15.

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Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables

2021-01-07

Muhammad Aamir Ali , Yu–Ming Chu , Hüseyin Budak +3 more

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Quantum Hermite–Hadamard inequality by means of a Green function

2020-03-02

Muhammad Adil Khan , Noor Mohammad , Eze R. Nwaeze +1 more

Abstract The purpose of this work is to present the quantum Hermite–Hadamard inequality through the Green function approach. While doing this, we deduce some novel quantum identities. Using these identities, … Abstract The purpose of this work is to present the quantum Hermite–Hadamard inequality through the Green function approach. While doing this, we deduce some novel quantum identities. Using these identities, we establish some new inequalities in this direction. We contemplate the possibility of expanding the method, outlined herein, to recast the proofs of some known inequalities in the literature.

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On the Ostrowski's integral inequality for mappings with bounded variation and applications

2001-01-01

Sever S Dragomir

A generalization of Ostrowski's inequality for mappings with bounded variation and applications in Numerical Analysis for Euler's Beta function is given. A generalization of Ostrowski's inequality for mappings with bounded variation and applications in Numerical Analysis for Euler's Beta function is given.

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On a new class of fractional operators

2017-08-22

Fahd Jarad , Ekin Uğurlu , Thabet Abdeljawad +1 more

This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related … This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.

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A new definition of fractional derivative

2014-01-16

Roshdi Khalil , Mohammed Al Horani , A. Yousef +1 more

We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The … We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for 0≤α<1 coincides with the classical definitions on polynomials (up to a constant). Further, if α=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.

On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals

2013-08-12

Mehmet Zeki Sarıkaya

In this paper, we initially present new some inequality of Hermite–Hadamard-type for co-ordinated convex functions on a rectangle from the plane ℝ2 via Riemann–Liouville fractional integrals. Then, we give an … In this paper, we initially present new some inequality of Hermite–Hadamard-type for co-ordinated convex functions on a rectangle from the plane ℝ2 via Riemann–Liouville fractional integrals. Then, we give an integral identity for fractional integrals and with the help of this integral identity we establish some integral inequalities with the right-hand side of the fractional Hermite–Hadamard-type inequality on the co-ordinates.

Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions

2022-03-21

Thanin Sitthiwirattham , Kamsing Nonlaopon , Muhammad Aamir Ali +1 more

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Some Fractional q-Integrals and q-Derivatives

1966-12-01

W. A. Al‐Salam

A q -analogue of the integral ∣ f(t)dt is defined by means of which is an inverse of the q –derivative The present author ( 2 ) has recently obtained … A q -analogue of the integral ∣ f(t)dt is defined by means of which is an inverse of the q –derivative The present author ( 2 ) has recently obtained a q –nalogue of a formula of Cauchy, namely, where, for real or complex α and N a positive integer,

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On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions

2019-07-17

Seksan Jhanthanam , Jessada Tariboon , Sotiris K. Ntouyas +1 more

In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of … In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.

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Some new inequalities of Simpson’s type for s-convex functions via fractional integrals

2017-01-01

Jianhua Chen , Xianjiu Huang

In this paper, we establish some new inequalities of Simpson?s type based on s-convexity via fractional integrals. Our results generalize the results obtained by Sarikaya et al. [1]. In this paper, we establish some new inequalities of Simpson?s type based on s-convexity via fractional integrals. Our results generalize the results obtained by Sarikaya et al. [1].

On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function

2016-03-30

Mohamed Jleli

In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function.Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function.Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals.

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On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals

2021-05-27

Hüseyin Budak , Fatih Hezenci , Hasan Kara

On generalized fractional integral inequalities for twice differentiable convex functions

2020-01-23

Pshtiwan Othman Mohammed , Mehmet Zeki Sarıkaya

New Inequalities of Hermite-Hadamard Type for Functions Whose Second Derivatives Absolute Values Are Convex and Quasi-Convex

2012-09-01

Mehmet Zeki Sarıkaya , Aziz Sağlam , Hüseyin Yıldırım

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality.Some applications for special means of real numbers are also … In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality.Some applications for special means of real numbers are also provided.

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Convex functions and the Hadamard inequality

1994-01-01

A. G. Azpeitia

The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of … The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type.

Quantum Ostrowski inequalities for q-differentiable convex functions

2016-01-01

Muhammad Aslam Noor , Muhammad Uzair Awan , Khalida Inayat Noor

In this paper, we establish a new quantum analogue of classical integral identity.Using this quantum integral identity, we derive some quantum analogues of Ostrowski type inequalities for q -differentiable convex … In this paper, we establish a new quantum analogue of classical integral identity.Using this quantum integral identity, we derive some quantum analogues of Ostrowski type inequalities for q -differentiable convex functions.

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On some new inequalities for differentiable co-ordinated convex functions

2012-02-15

Muhammad Amer Latif , Sever S Dragomir

Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in … Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in two variables are obtained. Mathematics Subject Classification (2000): 26A51; 26D15

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