On operator inequalities of some relative operator entropies

In our recent paper, we introduced the notions of relative operator (α,β)$(\alpha ,\beta )$-entropy and Tsallis relative operator (α,β)$(\alpha ,\beta )$-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)$(\alpha ,\beta )$-geometric mean introduced in Nikoufar et al. (2013) [14].