Some Best Possible Inequalities Concerning Certain Bivariate Means

TL;DR

This paper establishes sharp bounds for the Neuman-Sándor mean using weighted arithmetic means of two bivariate means, contributing new inequalities to the mathematical understanding of these means.

Contribution

It introduces new sharp inequalities that bound the Neuman-Sándor mean in terms of weighted arithmetic means, enhancing the theoretical framework of bivariate means.

Findings

Derived sharp bounds for the Neuman-Sándor mean.

Established inequalities involving weighted arithmetic means.

Enhanced understanding of relationships among bivariate means.

Abstract

In this paper, some inequalities of bounds for the Neuman-S\'{a}ndor mean in terms of weighted arithmetic means of two bivariate means are established. Bounds involving weighted arithmetic means are sharp.