Simpson Type Inequalities via $\varphi$-Convexity

TL;DR

This paper derives Simpson type inequalities for functions with derivatives that are $ ext{phi}$-convex, expanding the scope of integral inequalities in mathematical analysis.

Contribution

It introduces new Simpson inequalities applicable to $ ext{phi}$-convex functions, broadening the class of functions for which such inequalities are valid.

Findings

Established new Simpson type inequalities for $ ext{phi}$-convex functions.

Extended classical inequalities to a broader function class.

Provided theoretical bounds for integrals of $ ext{phi}$-convex functions.

Abstract

In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are $\varphi$-convex.