scholarly journals New Hermite-Hadamard type inequalities for convex mappings utilizing generalized fractional integrals

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2329-2344
Author(s):  
Hüseyin Budak
Keyword(s):  
Convex Function ◽  
Fractional Integrals ◽  
Convex Mappings ◽  
Hadamard Fractional Integrals

In this work, we first establish new Hermite-Hadamard inequalities for convex function utilizing fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some generalized midpoint and trapezoid type inequalities for these kinds of fractional integrals. The inequalities given in this paper provide generalizations of several results obtained in earlier works.

scholarly journals On Hermite-Hadamard Type Inequalities for s–Convex Mappings via Fractional Integrals of a Function with Respect to Another Function

2016 ◽  
Vol 57 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Z. Sarikaya
Keyword(s):  
Convex Function ◽  
Fractional Integrals ◽  
Convex Mappings ◽  
Hadamard Fractional Integrals

AbstractIn this paper, we obtain some Hermite-Hadamard type inequalities fors–convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.

scholarly journals Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Zhi Zhang ◽  
JinRong Wang ◽  
JianHua Deng
Keyword(s):  
Convex Function ◽  
Fractional Integral ◽  
Beta Function ◽  
Fractional Integrals ◽  
Incomplete Beta Function ◽  
Real Numbers ◽  
Special Means ◽  
New Type ◽  
Hadamard Fractional Integrals ◽  
Integral Identities

By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.

scholarly journals New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Saad Ihsan Butt ◽  
Saba Yousaf ◽  
Atifa Asghar ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Convex Function ◽  
Hypergeometric Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Convex Mappings ◽  
Special Means ◽  
Interesting Variation ◽  
Harmonically Convex Function ◽  
The Right ◽  
New Inequalities

In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

scholarly journals Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1503 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Artion Kashuri
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Important Direction ◽  
Increasing Function

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Hermite-Hadamard-Fejer type inequalities for s-convex function in the second sense via fractional integrals

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3131-3138 ◽  
Author(s):  
Erhan Set ◽  
İmdat İşcan ◽  
Hasan Kara
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals

In this paper, we established Hermite-Hadamard-Fejer type inequalities for s-convex functions in the second sense via fractional integrals. The some results presented here would provide extansions of those given in earlier works.

scholarly journals Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function

2021 ◽  
Vol 7 (1) ◽  
pp. 784-803
Author(s):  
Fangfang Ma ◽  
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Definition Of

<abstract><p>In this paper we find further versions of generalized Hadamard type fractional integral inequality for $ k $-fractional integrals. For this purpose we utilize the definition of $ h $-convex function. The presented results hold simultaneously for variant types of convexities and fractional integrals.</p></abstract>

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