Some Generalizations of Hermite-Hadamard type Integral Inequalities and their Applications

TL;DR

This paper develops generalized Hermite-Hadamard integral inequalities for differentiable functions with (h-($oldsymbol{ extalpha}$?;m))-convex derivatives, providing improved estimates and applications in numerical integration and special means.

Contribution

It introduces new generalized inequalities linked to (h-($oldsymbol{ extalpha}$?;m))-convexity, enhancing existing bounds and extending their applications.

Findings

Derived improved Hermite-Hadamard type inequalities for (h-($ extalpha$?;m))-convex functions.

Applied the inequalities to numerical integration methods.

Extended the inequalities to relate to special means.

Abstract

In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite- Hadamard integral inequality for mappings whose derivatives are (h -($\alpha$?;m))-convex.The generalized integral inequalities contribute some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.