Hermite--Hadamard type inequalities via differentiable $h_\varphi$-preinvex functions for Fractional Integrals

TL;DR

This paper introduces a new class of convex functions called $h_ ext{\varphi}$-preinvex functions and establishes Hermite--Hadamard type inequalities for them using fractional integrals, extending existing results.

Contribution

The paper defines $h_\varphi$-preinvex functions and derives new Hermite--Hadamard inequalities for these functions via fractional integrals, broadening the scope of convex analysis.

Findings

Established Hermite--Hadamard inequalities for $h_\varphi$-preinvex functions.

Extended classical inequalities to fractional integral context.

Provided special cases illustrating the inequalities.

Abstract

In this paper, we consider a new class of convex functions which is called $h_{\varphi}-$preinvex functions. We prove several Hermite--Hadamard type inequalities for differentiable $h_\varphi$-preinvex functions via Fractional Integrals. Some special cases are also discussed. Our results extend and improve the corresponding ones in the literature.