Inequalities related to Symmetrized Harmonic Convex Functions

TL;DR

This paper extends Hermite-Hadamard inequalities to symmetrized harmonic convex functions and explores related inequalities for harmonic h-convex functions, including products of such functions.

Contribution

It introduces new Hermite-Hadamard type inequalities for symmetrized harmonic convex functions and their products, expanding the theoretical framework.

Findings

Extended Hermite-Hadamard inequalities to symmetrized harmonic convex functions

Derived inequalities for harmonic h-convex functions

Established inequalities for products of harmonic convex functions

Abstract

In this paper, we extend the Hermite-Hadamard type $\dot{I}$scan inequality to the class of symmetrized harmonic convex functions. The corresponding version for harmonic h-convex functions is also investigated. Furthermore, we establish Hermite-Hadamard type inequalites for the product of a harmonic convex function with a symmetrized harmonic convex function.