Estimation of f-divergence and shannon entropy by levin-son type inequalities for higher order convex functions via taylor polynomial

In this paper, Levinson-type inequalities are generalized by using Taylor polynomial for the class of k-convex (k ≥ 3) functions. Bounds for the remainders in new generalized identities involving data points of two types are given by using Čebyšev, Grüss and Ostrowski-type inequalities. In seek of applications of our results to information theory, new generalizations based on f-divergence estimates are also proven. Moreover, some inequalities for Shannon entropies are deduced as well. © 2020, International Scientific Research Publications. All rights reserved.