Operator mean inequalities and Kwong functions

TL;DR

This paper explores inequalities involving operator means, linking Kwong functions with operator monotone functions, and provides examples demonstrating the practical applications of these theoretical results.

Contribution

It introduces a modified result connecting Kwong functions with operator monotone functions and extends inequalities for operator means with new analogs of geometric concavity.

Findings

Relation between Kwong functions and operator monotone functions established

Operator mean inequalities extended with geometric concavity analogs

Examples illustrating the application of main theoretical results

Abstract

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions. Operator mean inequalities provide some analogs of the geometric concavity property for Kwong functions, operator convex, and operator monotone functions. Moreover, we give our points across by way of some examples which show the usage of our main results.