GENERALIZED CSISZAR'S f-DIVERGENCE FOR LIPSCHITZIAN FUNCTIONS

We started with the generalization of the Csiszar'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 Renyi divergence and chi(2)-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.