Estimation of f-divergence and Shannon entropy by Levinson type inequalities via new Green’s functions and Lidstone polynomial

By using new Green’s functions and Lidstone interpolating polynomial, some new generalizations of Levinson type inequalities for (2 p+ 1) -convex functions are obtained. 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, The Author(s).