Norm inequalities related to the Heron and Heinz means

TL;DR

This paper introduces new inequalities involving operator means, specifically comparing Heron and Heinz means, and refines classical inequalities like Cauchy-Schwarz using convexity and L"owner matrices.

Contribution

It provides novel comparisons and generalizations of operator Heron and Heinz means, along with refined inequalities for the Cauchy-Schwarz inequality.

Findings

New inequalities for operator Heron and Heinz means

Generalizations of the difference version of Heinz means

Refinements of the Cauchy-Schwarz inequality

Abstract

In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference version of the Heinz means and further refinements of the Cauchy-Schwarz inequality. The techniques used to accomplish these results include convexity and L\"{o}wner matrices.