Some central moments inequalities with applications

TL;DR

This paper develops new inequalities involving central moments for real numbers, extending existing theorems, and applies these results to matrix theory and polynomial equations, offering refined bounds and insights.

Contribution

It introduces novel central moments inequalities for real numbers, extending prior theorems and providing applications in matrix theory and polynomial equations.

Findings

Derived a new inequality involving central moments for n real numbers

Extended Theorem 2.2 of Wolkowicz and Styan [18]

Provided refinements of existing inequalities by Sharma et al.

Abstract

In this paper, we first derive an inequality involving central moments for n real numbers, which in turn provides an extension of Theorem 2.2 of Wolkowicz and Styan [18]. Furthermore, we present refinements of various inequalities obtained by Sharma et al. [12-15] involving central moments for the case of n distinct integers. Moreover, we provide applications of our results in matrix theory and the theory of polynomial equations.