Operator inequalities associated with relative operator entropies

Abstract

In this paper, we introduce the notions of operator (α,β,γ)-mean, relative operator (α,β,γ)-entropy and Tsallis relative operator (α,β,γ)-entropy. We give upper and lower bounds of relative operator (α,β,γ)-entropy, relative operator (0,β,γ)-entropy and Tsallis relative operator (α,β,γ)-entropy. Our results are refinements and generalizations of some existing inequalities due to Furuichi, Zou and Nikoufar.