Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals

Abstract

In this work, we estimated the different entropies like Shannon entropy, Rényi divergences, Csiszár divergence by using Jensen’s type functionals. The Zipf’s–Mandelbrot law and hybrid Zipf’s–Mandelbrot law are used to estimate the Shannon entropy. The Abel–Gontscharoff Green functions and Fink’s Identity are used to construct new inequalities and generalized them for m-convex function.

Keywords

• m-convex function
• Jensen’s inequality
• Shannon entropy
• f- and Rényi divergence
• Fink’s identity
• Abel–Gontscharoff Green function