Mehmet Zeki Sarıkaya

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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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On some Hadamard-type inequalities for h-convex functions

2008-01-01

Mehmet Zeki Sarıkaya , Aziz Sağlam , Hüseyin Yıldırım

In this paper, some inequalities Hadamard-type for h -convex functions are given.We also proved some Hadamard-type inequalities for products of two h -convex functions. In this paper, some inequalities Hadamard-type for h -convex functions are given.We also proved some Hadamard-type inequalities for products of two h -convex functions.

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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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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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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

On the generalization of some integral inequalities and their applications

2011-06-04

Mehmet Zeki Sarıkaya , Nesip Aktan

Generalized Ostrowski type inequalities for local fractional integrals

2016-12-07

Mehmet Zeki Sarıkaya , Hüseyin Budak

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>.

(k,s)-Riemann-Liouville fractional integral and applications

2015-07-30

Mehmet Zeki Sarıkaya , Zoubir Dahmani , Mehmet Eyüp Ki̇ri̇ş

In this paper, we introduce a new approach on fractional integration, which generalizes the Riemann-Liouville fractional integral.We prove some properties for this new approach.We also establish some new integral inequalities … In this paper, we introduce a new approach on fractional integration, which generalizes the Riemann-Liouville fractional integral.We prove some properties for this new approach.We also establish some new integral inequalities using this new fractional integration.

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On New Inequalities via Riemann‐Liouville Fractional Integration

2012-01-01

Mehmet Zeki Sarıkaya , Hasan Öğünmez

We extend the Montgomery identities for the Riemann‐Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the … We extend the Montgomery identities for the Riemann‐Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the fractional integral using differentiable convex functions.

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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.

New some Hadamard's type inequalities for co-ordinated convex functions

2010-01-01

Mehmet Zeki Sarıkaya , M. Emіn Özdemіr , Sever S Dragomir +1 more

In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates. In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates.

On generalized fractional integral inequalities for twice differentiable convex functions

2020-01-23

Pshtiwan Othman Mohammed , Mehmet Zeki Sarıkaya

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.

On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals

2020-04-08

Pshtiwan Othman Mohammed , Mehmet Zeki Sarıkaya , Dumitru Băleanu

Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate … Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of λ -incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite–Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann–Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

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Extensions of certain integral inequalities on time scales

2007-08-02

Umut Mutlu Özkan , Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

Hermite–Hadamard type inequalities for conformable fractional integrals

2017-06-10

Muhammad Adil Khan , Tahir Ali , Sever S Dragomir +1 more

$$\left( p,q\right) $$ p , q -Hermite–Hadamard inequalities and $$\left( p,q\right) $$ p , q -estimates for midpoint type inequalities via convex and quasi-convex functions

2017-05-15

Mehmet Kunt , İmdat İşcan , Necmettin Alp +1 more

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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On generalized Grüss type inequalities for k-fractional integrals

2015-08-06

Erhan Set , Muharrem Tomar , Mehmet Zeki Sarıkaya

On the generalized Hermite-Hadamard inequalities

2020-06-15

Mehmet Zeki Sarıkaya , Fatma Ertuğral

In this paper, we present a new definition which generalized some significant well known fractional integral operators such as Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral, Katugampola fractional operators, conformable fractional … In this paper, we present a new definition which generalized some significant well known fractional integral operators such as Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral, Katugampola fractional operators, conformable fractional integral, Hadamard fractional integrals, etc. Then, using a general class of this generalized fractional integral operator, we establish new generalized fractional integral inequalities of Hermite-Hadamard type which cover the previously puplished results

On new inequalities of Hermite–Hadamard–Fejér type for convex functions via fractional integrals

2015-03-28

Erhan Set , İmdat İşcan , Mehmet Zeki Sarıkaya +1 more

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The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results

2014-12-01

Erhan Set , Mehmet Zeki Sarıkaya , M. Emіn Özdemіr +1 more

Abstract In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in … Abstract In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in the proofs is fairly elementary.

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On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

2013-05-01

Mehmet Zeki Sarıkaya , Erhan Set , M. Emіn Özdemіr

Abstract In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given. Abstract In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.

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New inequalities of Ostrowski's type for s-convex functions in the second sense with applications

2010-01-01

Erhan Set , M. Emіn Özdemіr , Mehmet Zeki Sarıkaya

In this paper, we establish some new inequalities of Ostrowski's type for functions whose derivatives in absolute value are the class of s-convex. Some applications for special means of real … In this paper, we establish some new inequalities of Ostrowski's type for functions whose derivatives in absolute value are the class of s-convex. Some applications for special means of real numbers are also provided. Finally, some error estimates for the midpoint formula are obtained.

On generalized some integral inequalities for local fractional integrals

2016-01-07

Mehmet Zeki Sarıkaya , Tuba Tunç , Hüseyin Budak

On weighted Čebyšev-Grüss type inequalities on time scales

2008-01-01

Mehmet Zeki Sarıkaya , Nesip Aktan , Hüseyin Yıldırım

In this study In this study

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Simpson type integral inequalities for generalized fractional integral

2019-05-02

Fatma Ertuğral , Mehmet Zeki Sarıkaya

Generalized Pompeiu type inequalities for local fractional integrals and its applications

2015-12-05

Samet Erden , Mehmet Zeki Sarıkaya

Hermite–Hadamard type inequalities for F-convex function involving fractional integrals

2018-12-01

Pshtiwan Othman Mohammed , Mehmet Zeki Sarıkaya

In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, … In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractional integrals and classical integrals.

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New inequalities of Opial type for conformable fractional integrals

2017-01-01

Mehmet Zeki Sarıkaya , Hüseyin Budak

Some New Inequalities of Hermite-Hadamard's Type

2010-09-30

Aziz Sağlam , Hüseyin Yıldırım , Mehmet Zeki Sarıkaya

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are … In this paper, we establish several new inequalities for some 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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Some new inequalities of Hermite-Hadamard type for $s$-convex functions

2015-01-01

Mehmet Zeki Sarıkaya , Mehmet Eyüp Ki̇ri̇ş

Some new results related of the left-hand side of the Hermite-Hadamard type inequalities for the class of mappings whose second derivatives at certain powers are s convex in the second … Some new results related of the left-hand side of the Hermite-Hadamard type inequalities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established.Also, some applications to special means of real numbers are provided.

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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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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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The solutions of then-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution

2004-11-01

Hüseyin Yıldırım , Mehmet Zeki Sarıkaya , Sermin Öztürk

SOME NEW HADAMARD’S TYPE INEQUALITIES FOR CO-ORDINATED M-CONVEX AND (ALPHA, M)-CONVEX FUNCTIONS

2011-02-01

M. Emіn Özdemіr , Erhan Set , Mehmet Zeki Sarıkaya

In this paper, we establish some new Hermite-Hadamard type inequalities for m-convex and (α,m)-convex functions of 2-variables on the co-ordinates. In this paper, we establish some new Hermite-Hadamard type inequalities for m-convex and (α,m)-convex functions of 2-variables on the co-ordinates.

On the Weighted Ostrowski-type Integral Inequality for Double Integrals

2011-09-06

Mehmet Zeki Sarıkaya , Hasan Öğünmez

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Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities

2017-01-01

Erhan Set , Mehmet Zeki Sarıkaya , Abdurrahman Gözpınar

In this present study, ﬁrstly we give some necessary deﬁnitions and some results related to Riemann-Liouville fractional and conformable fracti- onal integrals. Secondly, using the given deﬁnitions , we established … In this present study, ﬁrstly we give some necessary deﬁnitions and some results related to Riemann-Liouville fractional and conformable fracti- onal integrals. Secondly, using the given deﬁnitions , we established a new identity and Hermite-Hadamard type inequalities via conformable fractional integrals. Relevant connections of the results presented here with those earlier ones are also pointed out.

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New Inequalities for Local Fractional Integrals

2017-10-27

Hüseyin Budak , Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals

2016-03-23

Çetin Yıldız , M. Emіn Özdemіr , Mehmet Zeki Sarıkaya

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality. In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

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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.

Some new Chebyshev type inequalities for functions whose derivatives belongs to $$L_{p}$$ L p spaces

2014-12-17

M. Emіn Özdemіr , Erhan Set , Ahmet Ocak Akdemi̇r +1 more

On the Ostrowski type integral inequality for double integrals

2012-09-01

Mehmet Zeki Sarıkaya

Abstract In this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis. Abstract In this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

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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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Note on the Ostrowski Type Inequalities for Fractional Integrals

2014-01-14

Mehmet Zeki Sarıkaya , Hatice Filiz

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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On Hermite-Hadamard-Fejér type integral inequalities for generalized convex functions via local fractional integrals

2019-09-09

Mehmet Zeki Sarıkaya , Necmettin Alp

In this paper, we extend some estimates of the right hand side of a Hermite-Hadamard-Fejér type inequality for generalized convex functions whose derivatives absolute values are generalized convex via local … In this paper, we extend some estimates of the right hand side of a Hermite-Hadamard-Fejér type inequality for generalized convex functions whose derivatives absolute values are generalized convex via local fractional integrals.

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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INEQUALITIES OF HERMITE‐HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE m‐CONVEX

2010-01-01

Erhan Set , M. Emіn Özdemіr , Mehmet Zeki Sarıkaya

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite … Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Erhan Set, M. Emin Özdemir, Mehmet Zeki Sarikaya; INEQUALITIES OF HERMITE‐HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE m‐CONVEX. AIP Conf. Proc. 11 November 2010; 1309 (1): 861–863. https://doi.org/10.1063/1.3525219 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves

2025-04-18

Abdelkader Lamamri , Yazid Gouari , Zoubir Dahmani +2 more

In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The … In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contraction principle. The existence of at least one solution is then accomplished by applying Schauder fixed point theorem. The Ulam Hyers stability, with a limiting-case example, is also discussed. In a second part of our work, we use the tanh method to obtain a new travelling wave solution for the coupled system of Burgers using time and space Khalil derivatives. By bridging these two aspects, we aim to present an understanding of the system’s behaviour.

Simpson’s quadrature formula for third differentiable and s-convex functions

2024-10-29

Bouharket Benaissa , Noureddine Azzouz , Mehmet Zeki Sarıkaya

This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter $p\geq 1$ for various … This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter $p\geq 1$ for various convexity cases.

Refinements Jensen's Inequality and Some Their Applications

2024-09-27

Mehmet Zeki Sarıkaya

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Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

2024-09-04

Samet Erden , Mehmet Zeki Sarıkaya , Burçin Gökkurt Özdemir +1 more

Milne-Type Inequalities for $h$-Convex Functions

2024-08-15

Bouharket Benaissa , Mehmet Zeki Sarıkaya

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.

New Weighted Inequalities for Functions Whose Higher-Order Partial Derivatives Are Co-Ordinated Convex

2024-06-30

Samet Erden , Mehmet Zeki Sarıkaya

The purpose of this study is to establish recent inequalities based on double integrals of mappings whose higher-order partial derivatives in absolute value are convex on the co-ordinates on rectangle … The purpose of this study is to establish recent inequalities based on double integrals of mappings whose higher-order partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Also, some special cases of results improved in this study are examined.

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On a Sobolev Type Theorem for the Generalized Riesz Potential Generated by the Generalized Shift Operator on Morrey Space

2024-06-11

Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

In this paper, we give a generalized definition of Morrey space for Lebesgue measure. In this space, the inequality of Hardy-Sobolev type is established for the generalized Riesz potentials generated … In this paper, we give a generalized definition of Morrey space for Lebesgue measure. In this space, the inequality of Hardy-Sobolev type is established for the generalized Riesz potentials generated by the generalized shift operator. 2000 Mathematics Subject Classification. 31B10, 44A15

Discussion on (k, s)-RiemannLiouville fractional integral and applications

2024-04-14

Bouharket Benaissa , Mehmet Zeki Sarıkaya

In this paper we present the correct version of Theorem 2.2 in \cite{sarikaya} and prove it. In this paper we present the correct version of Theorem 2.2 in \cite{sarikaya} and prove it.

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On the refinements of some important inequalities with a finite set of positive numbers

2024-04-05

Bouharket Benaissa , Mehmet Zeki Sarıkaya

In this research, a novel method for enhancing the Hölder–Işcan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This … In this research, a novel method for enhancing the Hölder–Işcan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Hölder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function , an entirely new category of classical inequalities emerges for both Hölder and mean power inequalities.

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ON NEW REFINEMENTS AND GENERALIZATIONS OF q-HERMITE–HADAMARD INEQUALITIES FOR CONVEX FUNCTIONS

2024-04-01

Necmettin Alp , Hüseyin Budak , Mehmet Zeki Sarıkaya +1 more

We aim to prove generalized estimations for the q-Hermite–Hadamard inequality for convex functions using a parameter. By choosing this particular parameter, we show that our results reduce the previously obtained … We aim to prove generalized estimations for the q-Hermite–Hadamard inequality for convex functions using a parameter. By choosing this particular parameter, we show that our results reduce the previously obtained q-Hermite–Hadamard inequalities. We also present some new refinements of these q-Hermite–Hadamard inequalities. Furthermore, we establish a new lemma and, by using this lemma, we obtain some new quantum inequalities that generalize quantum midpoint and quantum trapezoid inequalities for convex functions.

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

2024-03-19

Kamel Bensassa , Zoubir Dahmani , Mahdi Rakah +1 more

Abstract In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the … Abstract In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam–Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end.

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A Three Fractional Order Jerk Equation With Anti Periodic Conditions

2024-01-30

Zoubir Dahmani , Meriem Mansouria Belhamiti , Mehmet Zeki Sarıkaya

We study a new Jerk equation involving three fractional derivatives and anti periodic conditions. By Banach contraction principle, we present an existence and uniqueness result for the considered problem. Then, … We study a new Jerk equation involving three fractional derivatives and anti periodic conditions. By Banach contraction principle, we present an existence and uniqueness result for the considered problem. Then, by applications of Krasnoselskii fixed point theorem, another result for the existence of at least one solution is established. Also, An illustrative example is discussed. At the end, an approximation for Caputo derivaitive is proposed and some chaotic behaviours are discussed by means of the Runge Kutta 4th order method.

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A Three Fractional Order Jerk EquationWith Anti Periodic Conditions

2024-01-30

Zoubir Dahmani , Meriem Mansouria Belhamiti , Mehmet Zeki Sarıkaya

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New results on symmetrized convex sequences

2024-01-01

Mohamed Amin Abdellaoui , Houda Mebarki , Zoubir Dahmani +1 more

In this article, we establish new inequalities involving symmetrized convex sequences.The obtained results involve a new range of applications that contains the set of convex sequences.Some applications are given at … In this article, we establish new inequalities involving symmetrized convex sequences.The obtained results involve a new range of applications that contains the set of convex sequences.Some applications are given at the end of this paper.

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HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL

2024-01-01

H.-P. CHENG , Dafang Zhao , Mehmet Zeki Sarıkaya

Fractional [Formula: see text]-calculus is considered to be the fractional analogs of [Formula: see text]-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) [Formula: see text]-integral operator is introduced. … Fractional [Formula: see text]-calculus is considered to be the fractional analogs of [Formula: see text]-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) [Formula: see text]-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving [Formula: see text]-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF [Formula: see text]-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.

Newton-type inequalities associated with convex functions via quantum calculus

2024-01-01

Waewta Luangboon , Kamsing Nonlaopon , Mehmet Zeki Sarıkaya +1 more

In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. … In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>q</mml:mi> <mml:mo class="MathClass-rel" stretchy="false">→</mml:mo> <mml:msup><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo class="MathClass-bin" stretchy="false">−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>. Finally, we give mathematical examples of convex functions to verify the newly established inequalities.

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Solvability for a coupled system of 4-sequential fractional differential equations

2024-01-01

Kamel Bensassa , Zoubir Dahmani , Mehmet Zeki Sarıkaya

The present work deals with a coupled system of fractional differential equations involving four sequential Caputo derivatives in each of its components.The fractional differential system gives rise to a standard … The present work deals with a coupled system of fractional differential equations involving four sequential Caputo derivatives in each of its components.The fractional differential system gives rise to a standard coupled system of two ordinary differential equations of order four, which has practical applications in some real-world phenomena such as robotics, aerospace, and electrical engineering.The existence of a unique vector solution for our sequential system is studied.The existence of at least one vector solution for the considered system is also investigated.Some illustrative examples are discussed in detail to show the main results' applicability.The stabilities in the sense of Ulam Hyers for the system is discussed.A conclusion follows at the end.

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Two numerical methods for solving conformable fractional KGE equation

2024-01-01

Ahmed Anber , Zoubir Dahmani , Mehmet Zeki Sarıkaya

The conformable fractional derivatives in the sense of Khalil is considered and the Homotopy analysis method and the (G’/G)-Expansion method are applied to solve the Klein-Gordon equation; new approximate solutions … The conformable fractional derivatives in the sense of Khalil is considered and the Homotopy analysis method and the (G’/G)-Expansion method are applied to solve the Klein-Gordon equation; new approximate solutions and new travelling wave solutions are obtained. Some numerical simulations are graphically illustrated. At the end, a conclusion is given.

New fractional integral extensions for inequalities involving monotone functions

2024-01-01

Zoubir Dahmani , Djamal Kaddar , Mehmet Zeki Sarıkaya

On some Grüss-type inequalities via k-weighted fractional operators

2024-01-01

Bouharket Benaissa , Noureddine Azzouz , Mehmet Zeki Sarıkaya

In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr?ss-type fractional integral inequalities. Furthermore, we … In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr?ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.

Some weighted Hermite-Hadamard type inclusions based on interval-valued convex and co-ordinated convex mappings

2024-01-01

Hasan Kara , Mehmet Zeki Sarıkaya , Hüseyin Budak

In this paper, we establish some Hermite-Hadamard inclusions for interval-valued convex functions and interval-valued co-ordinated convex functions by using interval-valued weighted function. The inclusions established in this work provide generalizations … In this paper, we establish some Hermite-Hadamard inclusions for interval-valued convex functions and interval-valued co-ordinated convex functions by using interval-valued weighted function. The inclusions established in this work provide generalizations of some results given in earlier works. As special cases, we give some new weighted Hermite-Hadamard type inclusions involving logarithmic function.

New regular perturbation for a sequential random differential problem of Airy type

2024-01-01

Houari Fettouch , Zoubir Dahmani , Mehmet Zeki Sarıkaya +1 more

In this paper, we study a new problem of random differential equations of Airy type by means of the stochastic mean square theory. A new perturbation problem is introduced and … In this paper, we study a new problem of random differential equations of Airy type by means of the stochastic mean square theory. A new perturbation problem is introduced and some existence and uniqueness results for ?stochastic process? solutions? are established. At the end, an example is discussed in details.

Hardy Type Inequalities for Convex Functions

2023-09-26

Mehmet Zeki Sarıkaya

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UNIQUENESS OF SOLUTIONS, STABILITY AND SIMULATIONS FOR A DIFFERENTIAL PROBLEM INVOLVING CONVERGENT SERIES AND TIME VARIABLE SINGULARITIES

2023-08-01

Yazid Gouari , Zoubir Dahmani , Meriem Mansouria Belhamiti +1 more

We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series … We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann–Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam–Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge–Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.

Hermite–Hadamard-type Inequalities for $$\hbar$$-preinvex Interval-Valued Functions via Fractional Integral

2023-07-26

Yun Tan , Dafang Zhao , Mehmet Zeki Sarıkaya

Abstract We present a comprehensive study on Hermite–Hadamard-type inequalities for interval-valued functions that are $$\hbar$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ħ</mml:mi> </mml:math> -preinvex, using the Riemann–Liouville fractional integral. Our research extends and generalizes … Abstract We present a comprehensive study on Hermite–Hadamard-type inequalities for interval-valued functions that are $$\hbar$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ħ</mml:mi> </mml:math> -preinvex, using the Riemann–Liouville fractional integral. Our research extends and generalizes some existing results found in the literature. In addition, we provide accurate proofs for the main theorems originally derived by Srivastava et al. in their publication titled “Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators" (Int. J. Comput. Int. Sys. 15(1):8, 2022). Finally, we illustrate our findings through a practical example to demonstrate the validity of our results.

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Diamond-alpha inequalities with two parameters on time scales

2023-07-03

Bouharket Benaissa , Mehmet Zeki Sarıkaya

In this article, we give a new version of n-tuple diamond-alpha H¨older inequality on time scales, this result generalizes some results known in the literature. Second, we present n-tuple diamond-alpha … In this article, we give a new version of n-tuple diamond-alpha H¨older inequality on time scales, this result generalizes some results known in the literature. Second, we present n-tuple diamond-alpha inequality with two parameters on time scales. It is a tool to generalize integral inequalities on time scales, its goal is to create an inequality restarted from the left side with a parameter to a right side with two parameters. Moreover, new Minkowski integral inequality with two parameters is given, and some interesting integral inequalities are found.

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Existence results for a hybrid system of mixed differential equations with sequential fractional derivatives

2023-06-14

Mehmet Zeki Sarıkaya , Hammou Benmehidi , Zoubir Dahmani

Abstract In this paper, we are interested in studying a hybrid system of sequential type by applying the Caputo and Hadamard fractional derivatives, using the fixed point principle, we establish … Abstract In this paper, we are interested in studying a hybrid system of sequential type by applying the Caputo and Hadamard fractional derivatives, using the fixed point principle, we establish new result for the existence and uniqueness of solutions. Another result is established by using Schaefer's fixed point theorem. At the end, an example is given. 2020 Mathematics Subject Classification. 30C45, 39B72, 39B85.

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Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule

2023-05-13

Hüseyin Budak , Fatih Hezenci , Hasan Kara +1 more

Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper … Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann–Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson’s inequalities is the first paper in the literature as a method.

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Two fractional order Langevin equation with new chaotic dynamics

2023-01-19

Meriem Mansouria Belhamiti , Zoubir Dahmani , Mehmet Zeki Sarıkaya

In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point … In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.

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On some new quantum trapezoid-type inequalities for q-differentiable coordinated convex functions

2023-01-11

Fongchan Wannalookkhee , Kamsing Nonlaopon , Mehmet Zeki Sarıkaya +2 more

Abstract In this paper, we establish several new inequalities for q -differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We … Abstract In this paper, we establish several new inequalities for q -differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results.

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q-Laplace Transform on Quantum Integral

2023-01-01

NECMETTIN ALP , Mehmet Zeki Sarıkaya

In this paper, we present q-Laplace transform by q-integral deﬁnition on quantum analogue. We present some properties and obtain formulaes of q-Laplace transform with its aplications. In this paper, we present q-Laplace transform by q-integral deﬁnition on quantum analogue. We present some properties and obtain formulaes of q-Laplace transform with its aplications.

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Quantum Hermite-Hadamard type inequalities and related inequalities for subadditive functions

2023-01-01

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

Ostrowski type inequalities for functions of two variables via generalized fractional integrals

2023-01-01

Kubilay Özçelik , Hüseyin Budak , Mehmet Zeki Sarıkaya +1 more

On the generalized Iyengar type inequalities

2023-01-01

Mehmet Zeki Sarıkaya

In the paper, we establish two inequalities for differentiable bounded functions and Lipschitzian function, which are connected with Iyengar integral inequalities, and we present some new results. In the paper, we establish two inequalities for differentiable bounded functions and Lipschitzian function, which are connected with Iyengar integral inequalities, and we present some new results.

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New parameterized inequalities for twice differentiable functions

2023-01-01

Hüseyin Budak , Hasan Kara , Fatih Hezenci +1 more

The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized … The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized inequalities for the functions whose second derivatives in absolute value are convex. Finally, we show that our main results reduce to trapezoid, midpoint Simpson and Bullen-type inequalities which are proved in earlier published papers.

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Generalized fractional midpoint type inequalities for co-ordinated convex functions

2023-01-01

Fatih Hezenci , Hüseyin Budak , Hasan Kara +1 more

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable … In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results.

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On the generalized Ostrowski type inequalities for co-ordinated convex functions

2023-01-01

Mehmet Zeki Sarıkaya

The purpose of this article is to establish some generalized Ostrowski type inequalities and integral inequalities in the coordinate plane for convex functions of 2 variables. For this, we will … The purpose of this article is to establish some generalized Ostrowski type inequalities and integral inequalities in the coordinate plane for convex functions of 2 variables. For this, we will specify a generalized identity, and with the help of this integral identity, we will examine the Ostrowski, trapezoid, and midpoint type integral inequalities, including Riemann integral and Riemann-Liouville fractional integral. In this way, we aim to contribute to the generalization of integral inequalities, an important topic in mathematical analysis.

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Opial-Jensen and functional inequalities for convex functions

2022-12-30

Mehmet Zeki Sarıkaya , Candan Can Bilişik

The main of this article are presenting generalized Opial type inequalities which will be defined as theOpial-Jensen inequality for convex function. Further, new Opial type inequalities will be given for … The main of this article are presenting generalized Opial type inequalities which will be defined as theOpial-Jensen inequality for convex function. Further, new Opial type inequalities will be given for functionalsdefined with the help of the Opial inequalities.

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"On the generalized trapezoid and midpoint type inequalities involving Euler's beta function}"

2022-12-19

Mehmet Zeki Sarıkaya , Gizem KOZAN

"The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler's beta function of Hermite-Hadamard type which cover the previously published result such as … "The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler's beta function of Hermite-Hadamard type which cover the previously published result such as Riemann integral, Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral."

Quantum ostrowski type inequalities for pre-invex functions

2022-12-01

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

On the Generalized Inequalities for Co-Ordinated Convex Functions

2022-11-01

Mehmet Zeki Sarıkaya

Abstract The aim of this paper is to establish some generalized integral inequalities for convex functions of 2-variables on the co-ordinat. Then, we will give a generalized identity and with … Abstract The aim of this paper is to establish some generalized integral inequalities for convex functions of 2-variables on the co-ordinat. Then, we will give a generalized identity and with the help of this integral identity, we will investigate some integral inequalities connected with the right hand side of the Hermite-Hadamard type inequalities involving Riemann integrals and Riemann-Liouville fractional integrals.

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On generalizations of trapezoid and Bullen type inequalities based on generalized fractional integrals

2022-10-25

Hüseyin Budak , Fatma Ertuğral , Muhammad Aamir Ali +3 more

<abstract><p>In this paper, we establish an integral identity involving differentiable functions and generalized fractional integrals. Then, using the newly established identity, we prove some new general versions of Bullen and … <abstract><p>In this paper, we establish an integral identity involving differentiable functions and generalized fractional integrals. Then, using the newly established identity, we prove some new general versions of Bullen and trapezoidal type inequalities for differentiable convex functions. The main benefit of the newly established inequalities is that they can be converted into similar inequalities for classical integrals, Riemann-Liouville fractional integrals, $ k $-Riemann-Liouville fractional integrals, Hadamard fractional integrals, etc. Moreover, the inequalities presented in the paper are extensions of several existing inequalities in the literature.</p></abstract>

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New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus

2022-07-20

Necmettin Alp , Hüseyin Budak , Samet Erden +1 more

On Feng Qi-type integral inequalities for local fractional integrals

2022-07-01

Abdullah Akkurt , Mehmet Zeki Sarıkaya , Hüzeyin Budak

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

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Some New Quantum Hermite–Hadamard Inequalities for Co-Ordinated Convex Functions

2022-06-07

Fongchan Wannalookkhee , Kamsing Nonlaopon , Sotiris K. Ntouyas +3 more

In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via q1,q2-integrals. Since the inequalities are newly proved, we therefore consider some examples of … In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via q1,q2-integrals. Since the inequalities are newly proved, we therefore consider some examples of co-ordinated convex functions and show their validity for particular choices of q1,q2∈(0,1). We hope that the readers show their interest in these results.

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On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals

2022-06-01

Hüseyin Budak , Candan Can Bilişik , Mehmet Zeki Sarıkaya

Some parameterized Simpson-, midpoint- and trapezoid-type inequalities for generalized fractional integrals

2022-04-11

Hüseyin Budak , Seda KILINÇ , Mehmet Zeki Sarıkaya +1 more

Abstract In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. … Abstract In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers.

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New quantum boundaries for q-Simpson's type inequalities for co-ordinated convex functions

2022-03-30

Necmettin Alp , Muhammad Aamir Ali , Hüseyin Budak +1 more

The aim of this work is to develop quantum estimates for q-Simpson type integral inequalities for co-ordinated convex functions by using the notion of newly defined q₁q₂-derivatives and integrals. For … The aim of this work is to develop quantum estimates for q-Simpson type integral inequalities for co-ordinated convex functions by using the notion of newly defined q₁q₂-derivatives and integrals. For this, we establish a new identity including quantum integrals and quantum numbers via q₁q₂- differentiable functions. After that, with the help of this equality, we achieved the results we want. The outcomes raised in this paper are extensions and generalizations of the comparable results in the literature on Simpson’s inequalities for co-ordinated convex functions.

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On new generalized quantum integrals and related Hermite-Hadamard inequalities

2022-03-30

Hasan Kara , Hüseyin Budak , Necmettin Alp +2 more

In this article, we introduce a new concept of quantum integrals which is called $^{\kappa_{2}}T_{q}$-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several … In this article, we introduce a new concept of quantum integrals which is called $^{\kappa_{2}}T_{q}$-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several Hermite-Hadamard type inequalities for $^{\kappa_{2}}T_{q}$-integral by utilizing differentiable convex functions. The results presented in this article are unification and generalization of the comparable results in the literature.

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Coauthor	Papers Together
Hüseyin Budak	117
Erhan Set	44
Hüseyin Yıldırım	43
Samet Erden	32
Zoubir Dahmani	27
Hatice Yaldız	26
M. Emіn Özdemіr	26
Fuat Usta	25
Necmettin Alp	20
Muhammad Aamir Ali	16
Tuba Tunç	16
Hakan Bozkurt	12
Fatma Ertuğral	11
Bouharket Benaissa	10
Aziz Sağlam	10
Hasan Kara	9
Mehmet Eyüp Kırış	9
Nesip Aktan	8
Abdullah Akkurt	8
Artion Kashuri	7
Candan Can Bilişik	6
Ahmet Ocak Akdemi̇r	6
Meriem Mansouria Belhamiti	6
Hasan Öğünmez	5
Kamsing Nonlaopon	5
İmdat İşcan	5
Filiz Karakoç	5
Mustafa Yıldız	5
Hüseyin BUDAK	4
Fatih Hezenci	4
Yazid Gouari	4
Kazım İlarslan	4
Zhiyue Zhang	4
Umut Mutlu Özkan	4
Mohamed Houas	3
Muharrem Tomar	3
Sever S Dragomir	3
Nuri Çelik	3
Pshtiwan Othman Mohammed	3
Fongchan Wannalookkhee	3
Hatice Öğülmüş	3
Mohamed Bezzıou	3
Kubilay Özçelik	3
Dafang Zhao	3
Noureddine Azzouz	2
H. Yildirim	2
Haticeyaldiz	2
İbrahim Günaltılı	2
Hatice Filiz	2
Humaira Kalsoom	2

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

�ber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert

1937-12-01

Alexander Ostrowski

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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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.

On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula

2003-08-07

U.S. Kirmaci , M. Emіn Özdemіr

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

2003-02-17

U.S. Kirmaci

On New Inequalities via Riemann‐Liouville Fractional Integration

2012-01-01

Mehmet Zeki Sarıkaya , Hasan Öğünmez

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Convex Functions, Partial Orderings, and Statistical Applications

1992-01-01

Josip ‎Pečarić , Frank Proschan , Y. L. Tong

On Minkowski and Hermite-Hadamard integral inequalities via fractional integration

2010-01-01

Zoubir Dahmani

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On some fractional q-Integral inequalities

2013-01-01

Kamel Brahima , Sabrina Tafb

In this paper, using the Riemann-Liouville fractional q-integral, we establish some new results of the In this paper, using the Riemann-Liouville fractional q-integral, we establish some new results of the

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.

Inequalities for differentiable mappings with application to special means and quadrature formulæ

2000-02-01

C. E. M. Pearce , Josip ‎Pečarić

Theory and Applications of Fractional Differential Equations

2006-01-01

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

Inequalities in Fractional Integrals

2013-03-01

Djemaïa Bensikaddour , Zoubir Dahmani

In this paper, we use the Riemann-Liouville fractional integral to present recent results on fractional integral inequalities. By considering the extended Chebyshev functional in the case of synchronous functions, we … In this paper, we use the Riemann-Liouville fractional integral to present recent results on fractional integral inequalities. By considering the extended Chebyshev functional in the case of synchronous functions, we establish two main results. The first one deals with some inequalities using one fractional parameter. The second result concerns others inequalities using two fractional parameters.

Hadamard-type inequalities for s-convex functions

2007-03-19

U.S. Kirmaci , Milica Klaričić Bakula , M. Emіn Özdemіr +1 more

Inequalities Involving Functions and Their Integrals and Derivatives

1991-01-01

D. S. Mitrinović , Josip ‎Pečarić , A. M. Fink

On conformable fractional calculus

2014-10-29

Thabet Abdeljawad

Some remarks ons-convex functions

1994-08-01

Henryk Hudzik , Lech Maligranda

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On the Weighted Ostrowski-type Integral Inequality for Double Integrals

2011-09-06

Mehmet Zeki Sarıkaya , Hasan Öğünmez

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On some Hadamard-type inequalities for h-convex functions

2008-01-01

Mehmet Zeki Sarıkaya , Aziz Sağlam , Hüseyin Yıldırım

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Some New Results on the New Conformable Fractional Calculus with Application Using D’Alambert Approach

2016-04-01

Olaniyi S. Iyiola , Eze R. Nwaeze

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 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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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.

On the Ostrowski type integral inequality for double integrals

2012-09-01

Mehmet Zeki Sarıkaya

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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

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NOTE ON SOME HADAMARD-TYPE INEQUALITIES

2004-01-01

M. Klari , C Bakula

Some Hadamard-type inequalities involving the product of two convex functions are obtained. Our results generalize the corresponding results of B.G.Pachpatte. Some Hadamard-type inequalities involving the product of two convex functions are obtained. Our results generalize the corresponding results of B.G.Pachpatte.

On the generalization of some integral inequalities and their applications

2011-06-04

Mehmet Zeki Sarıkaya , Nesip Aktan

SOME COMPANIONS OF AN OSTROWSKI TYPE INEQUALITY AND APPLICATIONS

2009-01-01

Zheng Liu

We establish some companions of an Ostrowski type integral inequality for functions whose derivatives are absolutely continuous. Applications for composite quadrature rules are also given. We establish some companions of an Ostrowski type integral inequality for functions whose derivatives are absolutely continuous. Applications for composite quadrature rules are also given.

Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method

2013-01-01

Yong-Ju Yang , Dumitru Băleanu , Xiao‐Jun Yang

The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very … The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.

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

2017-01-01

Mehmet Zeki Sarıkaya , Hüseyin Yıldırım

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On The Hadamard's Inequality for Log-Convex Functions on the Coordinates

2009-01-01

Mohammad W. Alomari , Maslina Darus

Inequalities of the Hadamard and Jensen types for coordinated log-convex functions defined in a rectangle from the plane and other related results are given. Inequalities of the Hadamard and Jensen types for coordinated log-convex functions defined in a rectangle from the plane and other related results are given.

The Ostrowski integral inequality for mappings of bounded variation

1999-12-01

Sever S Dragomir

A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given. A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.

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Generalized Convex Functions on Fractal Sets and Two Related Inequalities

2014-01-01

Huixia Mo , Xin Sui , Dongyan Yu

We introduce the generalized convex function on fractal sets<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mi>α</mml:mi></mml:msup><mml:mrow><mml:mo> (</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>of real line numbers and study the properties of the generalized convex function. Based on these properties, we … We introduce the generalized convex function on fractal sets<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mi>α</mml:mi></mml:msup><mml:mrow><mml:mo> (</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen’s inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.

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

2001-01-12

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.

ABEL'S FORMULA AND WRONSKIAN FOR CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS

2014-05-08

MALIKA HAMMAD , Roshdi Khalil

In this paper, we discuss and present the form of the Wronskian for conformable fractional linear differential equations with variable coefficients. Further, we prove that there is an Able's formula … In this paper, we discuss and present the form of the Wronskian for conformable fractional linear differential equations with variable coefficients. Further, we prove that there is an Able's formula for fractional differential equations with variable coefficients.

On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions

2010-01-01

Erhan Set , MEmin Özdemir , Sever S Dragomir

We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary … We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary and based on the use of the Minkowski, Hölder, and Young inequalities.

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Two mappings in connection to Hadamard's inequalities

1992-06-01

Sever S Dragomir

New inequalities of Ostrowski type for mappings whose derivatives are <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 in the second sense via fractional integrals

2011-12-30

Erhan Set

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A Companion of Ostrowski’s Inequality for Functions of Bounded Variation and Applications

2014-01-01

Sever S Dragomir

A companion of Ostrowski’s inequality for functions of bounded variation and applications are given. A companion of Ostrowski’s inequality for functions of bounded variation and applications are given.

A refinement of the companion of Ostrowski inequality for functions of bounded variation and applications

2012-01-01

Wenjun Liu , Yun Sun

In this paper we establish a refinement of the companion of Ostrowski inequality for functions of bounded variation. Applications for the trapezoid inequality, the mid-point inequality, and to probability density … In this paper we establish a refinement of the companion of Ostrowski inequality for functions of bounded variation. Applications for the trapezoid inequality, the mid-point inequality, and to probability density functions are also given.

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Local Fractional Integral Equations and Their Applications

2012-06-02

Xiao‐Jun Yang

This letter outlines the local fractional integral equations carried out by the local fractional calculus (LFC). We first introduce the local fractional calculus and its fractal geometrical explanation. We then … This letter outlines the local fractional integral equations carried out by the local fractional calculus (LFC). We first introduce the local fractional calculus and its fractal geometrical explanation. We then investigate the local fractional Volterra/ Fredholm integral equations, local fractional nonlinear integral equations, local fractional singular integral equations and local fractional integro-differential equations. Finally, their applications of some integral equations to handle some differential equations with local fractional derivative and local fractional integral transforms in fractal space are discussed in detail.

Classical and new inequalities in analysis

1993-12-01

D. S. Mitrinović , J. E. Pečarić , A. M. Fink

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Integral inequalities in q-calculus

2004-01-01

Hillel Gauchman

On a new Ostrowski type inequality in two independent variables

2001-03-31

B. G. Pachpatte

In this note a new integral inequality of Ostrowski type in two independent variables is established. The discrete analogue of the main result is also given. In this note a new integral inequality of Ostrowski type in two independent variables is established. The discrete analogue of the main result is also given.

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

2013-08-12

Mehmet Zeki Sarıkaya

Some perturbed Ostrowski type inequalities for functions of bounded variation

2015-08-19

Sever S Dragomir

In this paper, some general two parameters perturbed Ostrowski type inequalities for functions of bounded variation are established. In this paper, some general two parameters perturbed Ostrowski type inequalities for functions of bounded variation are established.

Stetigkeitsaussagen Für Eine Klasse Verallgemeinerter Konvexer Funktionen In Topologischen Linearen Räumen

1978-01-01

Wolfgang W. Breckner

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