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Generalized Csiszar's F-Divergence for Lipschitzian Functions

We started with the generalization of the Csisz ́ar’s f -divergence. We stated and proved Jensen’s type inequality for L-Lipschitzian functions. The results for commonly used examples of f-divergences, such as the Kullbach-Leibler divergence, the Hellinger divergence, the R ́enyi divergence and χ2 -distance are derived. Further, we examined two specific averaging functions, previously known in the literature. Finally, we obtained interesting results concerning the Zipf-Mandelbrot law.

f -divergence, Lipschitzian function, Zipf-Mandelbrot law

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