Refinement of Gini-Means Inequalities and Connections with Divergence Measures

TL;DR

This paper refines inequalities related to Gini means and Heron's mean, exploring their connections with divergence measures and improving existing bounds based on recent research.

Contribution

It introduces improved inequalities for Gini and Heron's means, extending their mathematical properties and linking them with divergence measures.

Findings

Enhanced bounds for Gini-Mean inequalities

Connections established between means and divergence measures

Improved mathematical inequalities based on recent results

Abstract

In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. It contains as particular cases the famous means such as harmonic, geometric, arithmetic, etc. Also it contains, the power mean of order r and Lehmer mean as particular cases. In this paper we have considered inequalities arising due to Gini-Mean and Heron's mean, and improved them based on the results recently studied by the author (Taneja, 2011).