  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.
