New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex

TL;DR

This paper develops new Hermite-Hadamard type inequalities for twice differentiable functions with convex or quasi-convex second derivatives, including applications to special means of real numbers.

Contribution

It introduces novel inequalities for functions with convex or quasi-convex second derivatives, extending Hermite-Hadamard inequalities and providing applications to means.

Findings

New inequalities for twice differentiable functions with convex second derivatives

Extensions to quasi-convex second derivatives

Applications to special means of real numbers

Abstract

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.