Mediterranean Journal of Mathematics, Volume (14), No (5), Year (2017-10) , Pages (1-18)

Title : ( Norm Inequalities Related to the Heron and Heinz Means )

Authors: Yogesh Kapil , Cristian Conde , Mohammad Sal Moslehian , Mandeep Singh , Mohammad Sababheh ,
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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.

Keywords

Norm inequality; Unitarily invariant norm; Operator mean; Heinz inequality; Normalized Jensen functional