New Generalized Hermite–Hadamard–Mercer’s Type Inequalities Using (k, ψ)-Proportional Fractional Integral Operator-Reference-Cited by-同舟云学术

New Generalized Hermite–Hadamard–Mercer’s Type Inequalities Using (k, ψ)-Proportional Fractional Integral Operator

Published:2023-01-11 Issue:1 Volume:3 Page:49-62
ISSN:2673-9321
Container-title:Foundations
language:en
Short-container-title:Foundations

Author:

Desta Henok Desalegn¹^ORCID,Nwaeze Eze R.²^ORCID,Abdi Tadesse¹^ORCID,Mijena Jebessa B.³

Affiliation:

1. Department of Mathematics, Addis Ababa University, Addis Ababa P.O. Box 1176, Ethiopia

2. Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA

3. Department of Mathematics, Georgia College & State University, Milledgeville, GA 31061, USA

Abstract

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.

Publisher

MDPI AG

Link

https://www.mdpi.com/2673-9321/3/1/5/pdf

Reference22 articles.

1. Hermite and convexity;Aequationes Math.,1985

2. Generalized convex functions;Beckenbach;Bull. Am. Math. Soc.,1937

3. Some new inequalities of the Hermite–Hadamard type for extended s-convex functions;Sun;J. Comput. Anal. Appl.,2019

4. Inequalities of the Hermite–Hadamard type for quasi-convex functions via the (k,s)-Riemann–Liouville fractional integrals;Nwaeze;Fract. Differ. Calc.,2018

5. Quantum Hermite–Hadamard inequality by means of a Green function;Khan;Adv. Differ. Equ.,2020

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