Some Hadamard and Simpson type integral inequalities via s-convexity and their applications

TL;DR

This paper develops generalized Hadamard and Simpson type integral inequalities using s-convexity, extending previous results and applying them to special means of positive real numbers with illustrative examples.

Contribution

It introduces new generalized inequalities based on s-convexity and applies them to special means, broadening the scope of existing integral inequalities.

Findings

Generalized Hadamard and Simpson inequalities derived

Applications to special means of positive real numbers demonstrated

Results extend previous inequalities in the literature

Abstract

In this study, we establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications to special means of positive real numbers are also given and generalized. Examples are given to show the results. The results generalize the integral inequalities in [11] and [13].