Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures

TL;DR

This paper introduces a new generalized triangular discrimination measure, explores inequalities among seven classical means, and presents new generating measures with exponential representations from a geometrical perspective.

Contribution

It proposes a novel generalized triangular discrimination measure and derives inequalities and exponential representations related to seven classical means.

Findings

Established inequalities among differences of seven classical means.

Introduced a new generalized triangular discrimination measure.

Presented new generating measures with exponential forms.

Abstract

From geometrical point of view, Eve (2003) studied seven means. These means are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal mean. We have considered for the first time a new measure calling generalized triangular discrimination. Inequalities among non-negative differences arising due to seven means and particular cases of generalized triangular discrimination are considered. Some new generating measures and their exponential representations are also presented.