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Levinson type inequalities are generalized by using Hermite interpolating polynomial for the class of $\mathfrak{n}$-convex functions. In seek of application to information theory, some estimates for new functional are obtained based on f divergence. Inequalities involving Shannon entropies are also discussed.

journal of inequalities and applications

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