Wigner--Yanase--Dyson function and logarithmic mean

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.