Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16125120240101Tsallis relative operator entropy properties with some weighted metrics556919046110.30504/jims.2024.435111.1157ENEl Hilali A.LAGA-Laboratory, Science Faculty, Ibn Tofail University, Kenitra, MoroccoM. CherguiDepartment of Mathematics, CRMEF-RSK, EREAM Team, LaREAMI-Lab, Kenitra, Morocco0000-0001-8077-2251Journal Article20240111The present work attempts to provide some properties for Tsallis relative operator entropy $T_p(A | B)$, acting on positive definite matrices, with respect to weighted Hellinger and Alpha Procrustes distances. Many localizations of this operator have been determined. In particular, some estimations of the distances between $T_p(A | B)$ and some standard matrix means are outlined.https://jims.ims.ir/article_190461_bcf219e78a7d13377778da4a3f78ff6f.pdf