Simpson Type Inequalities Via m- and (alpha,m)- logarithmically Convex functions

TL;DR

This paper establishes Simpson type inequalities for functions whose derivatives' absolute values are m- and (alpha,m)- logarithmically convex, expanding the scope of integral inequalities for convex functions.

Contribution

It introduces new Simpson type inequalities specifically for functions with derivatives that are m- and (alpha,m)- logarithmically convex, broadening existing convexity-based inequalities.

Findings

Derived new Simpson inequalities for m- and (alpha,m)- logarithmically convex functions.

Extended classical inequalities to broader classes of convex functions.

Provided bounds for integrals of functions with these convexity properties.

Abstract

In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are m- and (alpha,m)- logarithmically convex functions.