Generalized Csiszár's f-divergence for Lipschitzian functions

Abstract

. 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 χ 2 -distance are derived. Further, we examined two speci fi c averaging functions, previously known in the literature. Finally, we obtained interesting results concerning the Zipf-Mandelbrot law.