On Hermite-Hadamard Type Integral Inequalities for Functions Whose Second Derivative are nonconvex

TL;DR

This paper extends Hermite-Hadamard type inequalities to nonconvex functions with second derivatives that are -convex, log--convex, and quasi--convex, providing new bounds for these classes.

Contribution

It introduces new Hermite-Hadamard inequalities for functions with nonconvex second derivatives under various -convexity conditions.

Findings

Derived bounds for nonconvex functions with -convex second derivatives

Extended inequalities to log--convex and quasi--convex functions

Provided theoretical estimates for integral inequalities

Abstract

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are \phi-convex, log-\phi-convex, and quasi-\phi-convex.