New refinements of operator inequalities

Shigeru Furuichi, Hamid Reza Moradi, Mohammad Sababheh

Published 2018-01-25Version 1

New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary operator means. Furthermore, we obtain some new lower and upper bounds for the Tsallis relative operator entropy, operator monotone functions and positive linear maps.