Harmonically $m$-convex set-valued function

TL;DR

This paper introduces harmonically m-convex set-valued functions, combining harmonic m-convexity and set-valued functions, and explores their properties along with a Hermite-Hadamard type inequality.

Contribution

It defines a new class of functions, harmonically m-convex set-valued functions, and establishes foundational properties and inequalities for them.

Findings

Developed properties and characteristics of harmonically m-convex set-valued functions.

Established a Hermite-Hadamard type inequality for these functions.

Abstract

This research aimed to introduce the concept of harmonically m-convex set-valued functions, which is obtained from the combination of two definitions: harmonically m-convex functions and set-valued functions. In this work some properties and characteristics are developed, as well as a inequality of the Hermite-Hadamard type for such functions.