An extension of the P\'olya--Szeg\"o operator inequality

TL;DR

This paper extends a Pólya–Szegö operator inequality to general operator means and introduces additional related inequalities using the Mond–Pecaric method.

Contribution

It generalizes existing inequalities to broader operator means and develops new related inequalities with a novel methodological approach.

Findings

Extended Pólya–Szegö inequality to arbitrary operator means

Derived new related operator inequalities

Utilized Mond–Pecaric method for proofs

Abstract

We extend an operator P\'{o}lya--Szeg\"{o} type inequality involving the operator geometric mean to any arbitrary operator mean under some mild conditions. Utilizing the Mond--Pe\v{c}ari\'c method, we present some other related operator inequalities as well.