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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