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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 505184, 8 pages
http://dx.doi.org/10.1155/2014/505184
Research Article

A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization

1Department of Mathematics, College of Natural Sciences, Arba Minch University, Arab Minch, Ethiopia
2Department of Applied Sciences, Maharishi Markandeshwar University, Solan, Himachal Pradesh 173229, India

Received 3 September 2013; Revised 20 December 2013; Accepted 20 December 2013; Published 19 February 2014

Academic Editor: Chengjian Zhang

Copyright © 2014 Satish Kumar and Gurdas Ram. 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

In this communication, we characterize a measure of information of types , , and by taking certain axioms parallel to those considered earlier by Havrda and Charvat along with the recursive relation ( ; , , ) , ; , , ) ( ( )) , ; , ( )) , ; , ), , , , . Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case.