Hermite-Hadamard type inequalities via preinvexity and prequasiinvexity

TL;DR

This paper extends Hermite-Hadamard inequalities to functions with third derivatives that are preinvex or prequasiinvex, broadening the class of functions for which these inequalities hold.

Contribution

It introduces new Hermite-Hadamard type inequalities specifically for functions with third derivatives that are preinvex or prequasiinvex, which is a novel generalization.

Findings

Derived new inequalities for preinvex functions

Extended Hermite-Hadamard inequalities to prequasiinvex functions

Provided conditions under which these inequalities hold

Abstract

In this paper, we obtain some Hermite-Hadamard type inequalities for functions whose third derivatives in absolute value are preinvex and prequasiinvex.