Advances in Mathematical Physics
Volume 2011 (2011), Article ID 126108, 12 pages
http://dx.doi.org/10.1155/2011/126108
Research Article

Characterizations of Generalized Entropy Functions by Functional Equations

Shigeru Furuichi

Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo 156-8550, Japan

Received 3 March 2011; Revised 22 May 2011; Accepted 23 May 2011

Academic Editor: Giorgio Kaniadakis

Copyright © 2011 Shigeru Furuichi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that Tsallis entropy function is characterized by a functional equation, which is a different form that used by Suyari and Tsukada, 2009, that is, in a proposition 2.1 in the present paper. We give an interpretation of the functional equation in our main theorem.