Wigner--Yanase--Dyson function and logarithmic mean

TL;DR

This paper explores inequalities relating the Wigner--Yanase--Dyson function and logarithmic mean, providing reverse inequalities, comparisons with known bounds, and operator inequalities to deepen understanding of their mathematical relationships.

Contribution

The paper introduces new reverse inequalities for the Wigner--Yanase--Dyson function and logarithmic mean, expanding the theoretical framework and offering operator inequalities based on these results.

Findings

Derived two reverse inequalities for the Wigner--Yanase--Dyson function and logarithmic mean.

Compared new inequalities with existing bounds of the logarithmic mean.

Established operator inequalities based on the new inequalities.

Abstract

The ordering between Wigner--Yanase--Dyson function and logarithmic mean is known. Also bounds for logarithmic mean are known. In this paper, we give two reverse inequalities for Wigner--Yanase--Dyson function and logarithmic mean. We also compare the obtained results with the known bounds of the logarithmic mean. Finally, we give operator inequalities based on the obtained results.