Generalized csiszár’s f –divergence for lipschitzian functions

We started with the generalization of the Csiszár’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 Rényi 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. © 2021 Element D.O.O.. All rights reserved.