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On Jensen–Rényi and Jeffreys–Rényi type f-divergences induced by convex functions

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  • Kluza, Paweł A.

Abstract

In this paper, Rényi type f-divergences like Jensen–Rényi and Jeffreys–Rényi are studied for convex functions. Some comparison theorems for two divergences are provided. The obtained results imply for introduced divergences some new inequalities corresponding to nonnegative convex functions. Some examples of known entropies are introduced in order to show a few applications of new divergences.

Suggested Citation

  • Kluza, Paweł A., 2020. "On Jensen–Rényi and Jeffreys–Rényi type f-divergences induced by convex functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    • Handle: RePEc:eee:phsmap:v:548:y:2020:i:c:s0378437119314475
    DOI: 10.1016/j.physa.2019.122527
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    References listed on IDEAS

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    1. Furuichi, Shigeru & Mitroi, Flavia-Corina, 2012. "Mathematical inequalities for some divergences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 388-400.
    2. Ingram Olkin & Larry Shepp, 2013. "An inequality that subsumes the inequalities of Radon, Bohr, and Shannon," Annals of Operations Research, Springer, vol. 208(1), pages 31-36, September.
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