Document Type : Original Article
Department of Mathematics, CRMEF Rabat-Sale-Kenitra, EREAM Team, LaREAMI-Lab, Kenitra 14000, Morocco
Department of Mathematics, Faculty of Sciences, Ibn Tofail University, LAGA-Lab Kenitra, Morocco.
In this paper, we focus on geometric properties for relative operator entropy and its extensions for positive definite matrices by considering Riemannian metric. In particular, we prove that the Tsallis relative entropy $T_p(A|B)$ lies inside the sphere centered at the geometric mean of $A$ and $B$ with the radius equal to the half of the Riemannian distance between $A$ and $B$. Some numerical examples are given in the aim to verify the validity of the reverse of some results.