Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional

Abstract

The inequality containing Csiszár divergence on time scales is generalized for 2n2n-convex functions by using Lidstone interpolating polnomial. As an application, new entropic bounds on time scales are also computed. Several inequalities in quantum calculus and hh-discrete calculus are also established. The relationship between Shannon entropy, Kullback-Leibler divergence and Jeffreys distance with Zipf-Mandelbrot entropy are also established.