# On two new means of two arguments III

## TL;DR

This paper introduces two new means based on exponential functions and establishes inequalities for them, also refining existing inequalities involving the identric and logarithmic means.

## Contribution

It presents two novel means defined via exponential functions and derives inequalities for these means, extending and refining known inequalities involving classical means.

## Key findings

- Established two-sided inequalities for the new means X and Y.
- Refined existing inequalities involving the identric mean I.
- Extended the inequality framework for classical means.

## Abstract

In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic mean are refined from the literature as an application.