Mathematical inequalities for some divergences

Details Mathematical inequalities for some divergences Mathematical inequalities for some divergences

2011-04-29

arxiv.org/abs/1104.5603v2

Physica A 391 (2012) 388--400

Physics

Condensed Matter

Statistical Mechanics

18 pages

Scientific paper

10.1016/j.physa.2011.07.052

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.

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