  Divergences often play important roles for study in information science so
that it is indispensable to investigate their fundamental properties. There is
also a mathematical significance of such results. In this paper, we introduce
some parametric extended divergences combining Jeffreys divergence and Tsallis
entropy defined by generalized logarithmic functions, which lead to new
inequalities. In addition, we give lower bounds for one-parameter extended
Fermi-Dirac and Bose-Einstein divergences. Finally, we establish some
inequalities for the Tsallis entropy, the Tsallis relative entropy and some
divergences by the use of the Young's inequality.
