Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 307
On Some Estimations For A New Generalization Of Tsallis Relative Operator Entropy
Lahcen Tarik, Mohamed Chergui, Bouazza El Wahbi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 30, 2022
March 03, 2266
April 15, 2266

Abstract: In this work, we provide firstly a new generalization of the classical Hermite-Hadamard inequality. Then, we introduce a new operator T_(p,μ,ν)(A⁄B), that we call Tsallis mixed relative operator entropy, for two positive invertible operators defined on a complex Hilbert space. If μ=1 and ν=0, T_(p,μ,ν)(A⁄B) coincides with the well-known Tsallis relative operator T_p(A⁄B)[1-3]. We have been able to give this generalization, by virtue of some fundamental results of operator theory in particular those related to operator inequalities and operator means [4,5], for self-adjoint ...