Mathematical inequalities for some divergences
arXiv:1104.5603 · doi:10.1016/j.physa.2011.07.052
Abstract
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.
18 pages
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Cited by in corpus (7)
- Extropy: Complementary Dual of Entropy
- Refined Young inequality and its application to divergences
- On some properties of Tsallis hypoentropies and hypodivergences
- Some inequalities on generalized entropies
- Inequalities related to some types of entropies and divergences
- Failure extropy, dynamic failure extropy and their weighted versions
- Generalised Entropies and Metric-Invariant Optimal Countermeasures for Information Leakage under Symmetric Constraints