Inequalities related to some types of entropies and divergences

The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis quasilinear entropy and divergence by applying the Hermite-Hadamard inequality. We also give bounds for biparametrical extended entropies and divergences which have been given in \cite{7}. In addition, we study $(r,q)$-quasilinear entropies and divergences as alternative biparametrical 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.