Minkowski's inequality and sums of squares

TL;DR

This paper demonstrates that certain positive polynomials derived from classical inequalities like Minkowski's can be expressed as sums of squares, providing new insights into their algebraic structure.

Contribution

It introduces a novel approach to rewriting positive polynomials from classical inequalities as sums of squares, connecting inequality theory with algebraic representations.

Findings

Positive polynomials from Minkowski's inequality can be expressed as sums of squares.

The approach links classical inequalities with algebraic sum-of-squares representations.

Provides a new perspective on the structure of inequalities in polynomial form.

Abstract

Positive polynomials arising from Muirhead's inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski's inequality can be rewritten as sums of squares.