Journal of Mathematical Physics, Analysis, Geometry 2021, vol. 17, No 2, pp. 216-232   https://doi.org/10.15407/mag17.02.216     ( to contents , go back )

### Some Properties of the Tsallis Relative Operator φ-Entropy

Ismail Nikoufar

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
E-mail: nikoufar@pnu.ac.ir

Received February 26, 2020, revised March 10, 2021.

Abstract

In this paper, we introduce the notion of the Tsallis relative operator $\varphi$-entropy between two strictly positive operators and verify its properties such as joint convexity, joint subadditivity, and monotonicity. We also give the Shannon type operator inequality and its reverse one satisfied by the Tsallis relative operator $\varphi$-entropy.

Mathematics Subject Classification 2010: 81P45, 15A39, 47A63, 15A42, 81R15
Key words: perspective function, generalized perspective function, Tsallis relative operator entropy, Tsallis relative operator φ -entropy