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Hermite-Hadamard type fractional integral inequalities for generalized beta (r, g)-preinvex functions

Authors

Artion Kashuri, Rozana Liko
Type: Article
Publication Date: 2025-04-16
Citations: 0
DOI: https://doi.org/10.22199/issn.0717-6279-2544

Abstract

In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1]), [2]), but also provide new estimates on these types.

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Hermite-Hadamard type fractional integral inequalities for generalized beta ( r , g )-preinvex functions

2017-12-01
Artion Kashuri , Rozana Liko
In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving ā€¦ In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see (1), (2)), but also provide new estimates on these types.
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Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (r; g; s; m; Ļ•)-Preinvex Functions

2017-12-20
Artion Kashuri , Rozana Liko
Abstract In the present paper, a new class of generalized (r; g; s; m; Ļ•)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi ā€¦ Abstract In the present paper, a new class of generalized (r; g; s; m; Ļ•)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (r; g; s; m; Ļ•)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized (r; g; s; m; Ļ•)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1],[2]), but also provide new estimates on these types.

SOME NEW HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES TO PRODUCTS OF TWO GENERALIZED (r; g, s,m,\phi)-PREINVEX FUNCTIONS

2018-01-01
Artion Kashuri
In the present paper, a new class of generalized (r; g, s, m, Ļ•)preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature ā€¦ In the present paper, a new class of generalized (r; g, s, m, Ļ•)preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two generalized (r; g, s, m, Ļ•)-preinvex functions are given.Moreover, some generalizations of Hermite-Hadamard type inequalities to products of two generalized (r; g, s, m, Ļ•)-preinvex functions via Riemann-Liouville fractional integrals are established.These general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities and also extend some results appeared in the literature (see [1]).Some conclusions and future research are also given.

Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (r;s,m,varphi)-preinvex Functions

2017-04-20
Artion Kashuri , Rozana Liko
In the present paper, a new class of generalized $(r;s,m,\varphi)$-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized ā€¦ In the present paper, a new class of generalized $(r;s,m,\varphi)$-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized $(r;s,m,\varphi)$-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $(r;s,m,\varphi)$-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see \cite{AkRl}, \cite{AkYil}), but also provide new estimates on these types.

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; Ī¾)-preinvex functions

2017-06-27
Artion Kashuri , Rozana Liko
Abstract In this paper, the notion of generalized (s; m; Ī¾)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized ā€¦ Abstract In this paper, the notion of generalized (s; m; Ī¾)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; Ī¾)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; Ī¾)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.
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HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE GENERALIZED ${(s,m,\varphi)}$-PREINVEX FUNCTIONS

2017-10-15
Artion Kashuri , Rozana Liko
In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized $(s,m,\varphi)$-preinvex ā€¦ In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized $(s,m,\varphi)$-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $(s,m,\varphi)$-preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given.

HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED (1, m, )-PREINVEX FUNCTIONS

2017-03-10
Artion Kashuri , Rozana Liko
In the present paper, by using new identity for fractional integrals, some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized ( )preinvex -, , 1 ā€¦ In the present paper, by using new identity for fractional integrals, some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized ( )preinvex -, , 1 Ļ• m functions via Riemann-Liouville fractional integral are established.At the end, some applications to special means are given.

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

2017-08-25
Artion Kashuri , Rozana Liko
In the present paper, by using new identity for fractional integrals some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized (s, m, Ļ•)-preinvex functions via ā€¦ In the present paper, by using new identity for fractional integrals some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized (s, m, Ļ•)-preinvex functions via Riemann-Liouville fractional integral are established.These results not only extend the results appeared in the literature (see [2]), but also provide new estimates on these types.At the end, some applications to special means are given.
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Properties and Riemann-Liouville fractional Hermite-Hadamard inequalities for the generalized ( Ī± , m ) $(\alpha,m)$ -preinvex functions

2016-11-25
Tingsong Du , Jiagen Liao , LianZi Chen +1 more
The authors first introduce the concepts of generalized $(\alpha,m)$ -preinvex function, generalized quasi m-preinvex function and explicitly $(\alpha, m)$ -preinvex function, and then provide some interesting properties for the newly ā€¦ The authors first introduce the concepts of generalized $(\alpha,m)$ -preinvex function, generalized quasi m-preinvex function and explicitly $(\alpha, m)$ -preinvex function, and then provide some interesting properties for the newly introduced functions. The more important point is that we give a necessary and sufficient condition respecting the relationship between the generalized $(\alpha, m)$ -preinvex function and the generalized quasi m-preinvex function. Second, a new Riemann-Liouville fractional integral identity involving twice differentiable function on m-invex is found. By using this identity, we establish the right-sided new Hermite-Hadamard-type inequalities via Riemann-Liouville fractional integrals for generalized $(\alpha,m)$ -preinvex mappings. These inequalities can be viewed as generalization of several previously known results.
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Hermite-Hadamard type fractional integral inequalities for products of two MT(r;g,m,Ļ†)-preinvex functions

2020-02-04
Artion Kashuri , Rozana Liko
A new class of MT(r;g,m,Ļ†)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two MT(r;g,m,Ļ†)-preinvex functions are given. ā€¦ A new class of MT(r;g,m,Ļ†)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two MT(r;g,m,Ļ†)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for products of two MT(r;g,m,Ļ†)-preinvex functions via Riemann-Liouville fractional integrals are established. These general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities. At the end, some conclusions and future research are given.
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Hermite-Hadamard Type Inequalities for Mtm-Preinvex Functions

2017-07-26
Artion Kashuri , Rozana Liko
Abstract In the present paper, the notion of MT m -preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT ā€¦ Abstract In the present paper, the notion of MT m -preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT m -preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT m -preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These results not only extend the results appeared in the literature (see [13]), but also provide new estimates on these types.

On Hermite-Hadamard type inequalities for generalized (s,m,Ļ•)-preinvex functions via k-fractional integrals

2017-02-16
Artion Kashuri , Rozana Liko
In the present paper, the notion of generalized (s,m,Ļ•)-preinvex function is applied for establish some new Hermite-Hadamard type inequalities by using new identity for k-fractional Riemann-Liouville integrals. At the end, ā€¦ In the present paper, the notion of generalized (s,m,Ļ•)-preinvex function is applied for establish some new Hermite-Hadamard type inequalities by using new identity for k-fractional Riemann-Liouville integrals. At the end, some applications to special means are given. These results provide new estimates on these Hermite-Hadamard type inequalities via k-fractional Riemann-Liouville integrals.

Hermite-Hadamard type inequalities for generalized $(s, m, Ļ†)$-preinvex functions via $k$-fractional integrals

2017-09-01
Artion Kashuri , Rozana Liko
In the present paper, the notion of generalized $(s, m, Ļ†)$-preinvex function is applied to establish some new Hermite-Hadamard type inequalities via $k$-fractional Riemann-Liouville integrals. At the end, some applications ā€¦ In the present paper, the notion of generalized $(s, m, Ļ†)$-preinvex function is applied to establish some new Hermite-Hadamard type inequalities via $k$-fractional Riemann-Liouville integrals. At the end, some applications to special means are given. These results not only extend the results appeared in the literature, but also provide new estimates on these types.
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Fractional inequalities for exponentially generalized (m,Ļ‰,h_1,h_2)-preinvex functions with applications

2020-01-01
Artion Kashuri , Mehmet Kunt
The aim of this paper is to introduce a new extension of preinvexity called exponentially generalized (m,Ļ‰,h 1 ,h 2 ) -preinvexity.Some new integral inequalities of Hermite-Hadamard type for exponentially ā€¦ The aim of this paper is to introduce a new extension of preinvexity called exponentially generalized (m,Ļ‰,h 1 ,h 2 ) -preinvexity.Some new integral inequalities of Hermite-Hadamard type for exponentially generalized (m,Ļ‰,h 1 ,h 2 ) -preinvex functions via Riemann-Liouville fractional integral are established.We show that the class of exponentially generalized (m,Ļ‰,h 1 ,h 2 ) -preinvex functions includes several other classes of preinvex functions.At the end, some new error estimates for trapezoidal quadrature formula are provided as well.This results may stimulate further research in different areas of pure and applied sciences.
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More results on integral inequalities for strongly generalized ( Ļ• , h , s ) $( \phi,h,s )$ -preinvex functions

2019-04-18
Shahid Qaisar , Jamshed Nasir , Saad Ihsan Butt +1 more
The main goal of this research is to introduce a new form of generalized Hermiteā€“Hadamard and Simpson type inequalities utilizing Riemannā€“Liouville fractional integral by a new class of preinvex functions ā€¦ The main goal of this research is to introduce a new form of generalized Hermiteā€“Hadamard and Simpson type inequalities utilizing Riemannā€“Liouville fractional integral by a new class of preinvex functions which is known as strongly generalized $( \phi,h,s )$ -preinvex functions in the second sense. It is observed that the derived inequalities are generalizations of the inequalities obtained by W. Liu, W. Wen (Filomat 30(2):333ā€“342, 2016).
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Some new Hermite-Hadamard Type Conformable Fractional Integral Inequalities for Twice Differentiable MT_(r;g,m,\varphi)-preinvex Functions

2017-07-11
Akli Fundo , Artion Kashuri , Miftar RamosaƧo +1 more
In the present paper, the notion of MT_(r;g,m,\varphi)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT_(r;g,m,\varphi)-preinvex functions are given. ā€¦ In the present paper, the notion of MT_(r;g,m,\varphi)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT_(r;g,m,\varphi)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT_(r;g,m,\varphi)-preinvex functions that are twice differentiable via conformable fractional integrals are established. At the end, some applications to special means are given.

ON SOME FRACTIONAL INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR r-PREINVEX FUNCTIONS

2016-08-15
Abdullah Akkurt , HĆ¼seyin Yıldırım
In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals. In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

On some <i>k</i>-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (<i>r</i>, <i>g</i>)-preinvex functions

2019-05-21
Artion Kashuri , Rozana Liko
Abstract In the present paper, a new class of generalized beta <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>g</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> {(r,g)} -preinvex functions is introduced and some new integral ā€¦ Abstract In the present paper, a new class of generalized beta <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>g</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> {(r,g)} -preinvex functions is introduced and some new integral inequalities for the left-hand side of Gaussā€“Jacobi type quadrature formula involving generalized beta <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>g</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> {(r,g)} -preinvex functions are given. Moreover, some generalizations of Hermiteā€“Hadamard type inequalities for generalized beta <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>r</m:mi> <m:mo>,</m:mo> <m:mi>g</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> {(r,g)} -preinvex functions that are twice differentiable via k -fractional integrals are established. These general inequalities give us some new estimates for Hermiteā€“Hadamard type k -fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>Ļ†</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> (s,m,\varphi) -preinvex functions, Aust. J. Math. Anal. Appl. 13 2016, 1, Article ID 16]. At the end, some applications to special means are given.

Some inequalities of Hermiteā€“Hadamard, Ostrowski and Simpson type for (Ī¾,m,MT)-preinvex functions

2018-07-20
Leila Nasiri , Mahmood Shakoori
In this paper, we first introduce a new class of [Formula: see text]-preinvex functions, which are called [Formula: see text]-preinvex functions, then we give some new estimates of Hermiteā€“Hadamard, Ostrowski ā€¦ In this paper, we first introduce a new class of [Formula: see text]-preinvex functions, which are called [Formula: see text]-preinvex functions, then we give some new estimates of Hermiteā€“Hadamard, Ostrowski and Simpson type inequalities using Riemannā€“Liouville fractional integral. The obtained results in this paper generalize the well-known results in recent years.

Hermite-Hadamard Type Inequalities for Preinvex Functions via Right Riemann-Liouville Fractional Integrals

2020-07-28
Serap Ɩzcan
In this paper, with a new approach, some new Hermite-Hadamard type inequalities for preinvex functions are obtained by using only the right Riemann-Liouville fractional integrals. Our results generalize previous studies. ā€¦ In this paper, with a new approach, some new Hermite-Hadamard type inequalities for preinvex functions are obtained by using only the right Riemann-Liouville fractional integrals. Our results generalize previous studies. Results proved in this paper may stimulate further research in this field.