Nesbitt and Shapiro Cyclic Sum Inequalities for Positive Definite Matrices

TL;DR

This paper extends classical number theoretic inequalities by Nesbitt and Shapiro to the matrix setting, establishing noncommutative versions involving positive definite matrices.

Contribution

It introduces noncommutative counterparts of Nesbitt and Shapiro inequalities for positive definite matrices, expanding their applicability.

Findings

Established matrix versions of Nesbitt and Shapiro inequalities

Demonstrated noncommutative inequalities hold for positive definite matrices

Extended classical inequalities to the matrix setting

Abstract

The aim of this note is to show that certain number theoretic inequalities due to Nesbitt and Shapiro have noncommutative counterparts involving positive definite matrices.