On operator inequalities of some relative operator entropies

In our recent paper, we introduced the notions of relative operator (α,β)(α,β)-entropy and Tsallis relative operator (α,β)(α,β)-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)(α,β)-geometric mean introduced in Nikoufar et al. (2013) [14].