Simpson type inequalities for functions whose third derivatives in the absolute value are s-convex and s-concave

TL;DR

This paper develops new Simpson-type inequalities for functions whose third derivatives' absolute values are either s-convex or s-concave, expanding the theoretical framework for such inequalities.

Contribution

It introduces novel Simpson inequalities specifically for functions with third derivatives' absolute values exhibiting s-convexity or s-concavity, which was not previously addressed.

Findings

Derived new inequalities for s-convex functions

Extended Simpson inequalities to s-concave functions

Provided theoretical bounds for these classes of functions

Abstract

In this paper, we established some new inequalities via s-convex and s-concave functions.