Inequalities related to some types of entropies and divergences

03/20/2019

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by   Shigeru Furuichi, et al.

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The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a sereis of our studies for mathematical properties on entropy and divergence, we give new bounds for Tsallis quasilinear entropy and divergence by applying Hermite-Hadamard inequality. We also give bounds for two parameter-extended entropy and digergence which have been given in the previous paper by the first author. In addition, we introduce (r,q)-quasilinear entropy and divergence as alternative two parameter-extended entropy and divergence, and then we give bounds for them. Finally we obtain inequalities for an extended Lin's divergence and some characterizations of Fermi-Dirac entropy and Bose-Einstein entropy.