Inequalities for Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal Type f–Divergences

Abstract

In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.

Distance in Information and Statistical Physics III

“…Among many types of f -divergence, Kluza [5] introduces Jensen-Sharma-Mittal and Jeffreys-Sharma-Mittal divergences and shows their properties, including the lower and upper bounds. These divergences are extensions of Sharma-Mittal-type divergences, in which two parameters are contained, and they are the generalizations of Rényi, Tsallis, and Kullback-Leibler types with suitable choices of divergence functions.…”