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

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