Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 1 2024 01 01 Tsallis relative operator entropy properties with some weighted metrics 55 69 190461 10.30504/jims.2024.435111.1157 EN El Hilali A. LAGA-Laboratory, Science Faculty, Ibn Tofail University, Kenitra, Morocco M. Chergui Department of Mathematics, CRMEF-RSK, EREAM Team, LaREAMI-Lab, Kenitra, Morocco 0000-0001-8077-2251 Journal Article 2024 01 11 The 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_811dfdb67bb25b831778029b07a9e9f9.pdf