On Hadamard Type Integral Inequalities for nonconvex Functions

TL;DR

This paper extends Hermite-Hadamard type inequalities to nonconvex functions with -convex and quasi--convex derivatives, broadening the applicability of integral inequalities in mathematical analysis.

Contribution

It introduces new estimates for Hermite-Hadamard inequalities applicable to nonconvex functions with -convex derivatives, expanding existing theoretical frameworks.

Findings

Derived bounds for nonconvex functions with -convex derivatives

Extended Hermite-Hadamard inequalities to broader classes of functions

Provided theoretical estimates for integral inequalities in nonconvex settings

Abstract

In this paper, we extend some estimates of the right and left hand side of a Hermite-Hadamard type inequality for nonconvex functions whose derivatives absolute values are \Phi-convex and quasi-\Phi-convex was introduced by Noor in Noor1.