Copyright © 2012 Satish Kumar et al. 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.
We give an optimality characterization of nonadditive
generalized mean-value entropies from suitable nonadditive and generalized
mean-value properties of the measure of average length. The results obtained
cover many results obtained by other authors as particular cases, as well as the
ordinary length due to Shannon 1948. The main instrument is the function
of the word lengths in obtaining the average length of the code.