Some Generalization of Hadamard's type Inequalities through Differentiability for s-Convex Function and their Applications

TL;DR

This paper develops generalized Hermite-Hadamard type inequalities for s-convex functions with differentiability and absolute continuity, providing improved estimates and applications in numerical integration and means.

Contribution

It introduces a new form of integral inequalities for s-convex functions with derivatives that are absolutely continuous, enhancing existing bounds.

Findings

Derived generalized Hermite-Hadamard inequalities for s-convex functions.

Provided improved bounds over existing inequalities.

Applied inequalities to numerical integration and special means.

Abstract

In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral inequalities contributes some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.