IJPAM: Volume 51, No. 4 (2009)

TSALLIS RELATIVE ENTROPY
FOR CONVEX FUNCTIONALS

Mustapha Raïssouli
AFACSI Laboratory
Department of Mathematics and Informatics
Faculty of Sciences
Moulay Ismaïl University
P.O. Box 11201, Zitoune, Meknès, MOROCCO
e-mail: raissouli_10@hotmail.com


Abstract.The fundamental goal of this article is to introduce an extension of the Tsallis relative entropy,

\begin{displaymath}T_p(A/B)=\displaystyle\frac{A^{1/2}\left(A^{-1/2}BA^{-1/2}\right)^pA^{1/2}-A}{p},\end{displaymath}

from positive operators to convex functionals. Several results together with their proofs, already stated for relative operator entropy, are here obtained immediately in a fast way.

Received: January 31, 2009

AMS Subject Classification: 39B62, 54C70, 46S20

Key Words and Phrases: positive operator, convex functional relative operator entropy, relative functional entropy, Tsallis relative entropy, parameterized functional entropy

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 4