New Hermite-Hadamard and Simpson Type Inequalities For Harmonically $(s,m)$-convex functions in Second Sense

TL;DR

This paper introduces new inequalities of Hermite-Hadamard and Simpson type for harmonically $(s,m)$-convex functions in the second sense, expanding the scope of convexity-based inequalities.

Contribution

It generalizes existing inequalities to a broader class of harmonically $(s,m)$-convex functions, unifying various convexity concepts.

Findings

Derived new Hermite-Hadamard inequalities for harmonically $(s,m)$-convex functions

Established Simpson type inequalities for this class of functions

Extended the applicability of convexity inequalities to more general functions

Abstract

In \cite{II}, authors introduced the concept of harmonically $(s,m)$-convex functions in second sense which unifies different type of convexities and is more general notion of Harmonic convexity. In this paper, authors obtain new estimates on generalization of Hermite-Hadamard and Simpson type inequalities for this larger class of functions.