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

TL;DR

This paper extends Hermite-Hadamard inequalities to s-convex and m-convex functions using fractional integrals, and explores related Hadamard type inequalities with connections to KBOP.

Contribution

It introduces new Hermite-Hadamard inequalities for s-convex and m-convex functions via fractional integrals, expanding classical results.

Findings

Established Hermite-Hadamard inequalities for s-convex functions via fractional integrals.

Derived Hadamard type inequalities for fractional integrals.

Explored relationships with KBOP.

Abstract

In this paper, firstly we have established Hermite-Hadamard's inequalities for s-convex functions in the second sense and m-convex functions via fractional integrals. Secondly, a Hadamard type integral inequality for the fractional integrals are obtained and these result have some relationships with KBOP.