Gasparyan's Inequality

TL;DR

This paper presents a simplified proof of Gasparyan's inequality, originally based on complex hyperdeterminants, using standard mean inequalities and Gini means, making the proof more accessible.

Contribution

It introduces a more straightforward proof of Gasparyan's inequality utilizing classical inequalities and Gini means, replacing complex algebraic methods.

Findings

Simpler proof of Gasparyan's inequality

Use of Gini means in inequality proofs

Discussion of corollaries and open problems

Abstract

We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics such as mean inequalities. The main theorem on Gini means is essentially used. Some corollaries and problems are considered.