Generalisations of Integral Inequalities of Hermite-Hadamard type through Convexity

TL;DR

This paper develops new generalized Hermite-Hadamard type integral inequalities for differentiable functions with $s$-$(eta,m)$-convex derivatives, providing improved bounds and applications to numerical integration and means.

Contribution

It introduces novel generalized inequalities for $s$-$(eta,m)$-convex functions, extending classical Hermite-Hadamard inequalities with better estimates.

Findings

Derived improved integral inequalities for $s$-$(eta,m)$-convex functions.

Applied the inequalities to numerical integration methods.

Connected the results to special means and their bounds.

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 $s$-$(\alpha,m)$-convex.The generalised integral inequalities contribute some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.