Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial

Muhammad Adeel, Khuram Ali Khan, Ðilda Pečarić, Josip Pečarić
2020 Journal of Mathematics and Computer Science  
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 usinǧ Cebyšev, 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.
doi:10.22436/jmcs.021.04.05 fatcat:l4iuvxkmtnbm5cjxhe6pdilzim