%0 Journal Article %T Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial %A Adeel, Muhammad %A Khan, Khuram Ali %A Pečarić, Ðilda %A Pečarić, Josip %J Journal of Mathematics and Computer Science %D 2020 %V 21 %N 4 %@ ISSN 2008-949X %F Adeel2020 %X In this paper, Levinson-type inequalities are generalized by using Taylor polynomial for the class of \(k\)-convex \((k \geq 3)\) functions. Bounds for the remainders in new generalized identities involving data points of two types are given by using Čebyšev, Grúss 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. %9 journal article %R 10.22436/jmcs.021.04.05 %U http://dx.doi.org/10.22436/jmcs.021.04.05 %P 322--334 %0 Journal Article %T Generalization of the Levinson inequality with applications to information theory %A M. Adeel %A K. A. Khan %A Ð. Pečarić %A J. Pečarić %J J. Inequal. Appl. %D 2019 %V 2019 %F Adeel2019 %0 Journal Article %T Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation %A M. Adeel %A K. A. Khan %A Ð. Pečarić %A J. Pečarić %J Adv. Difference Equ. %D 2019 %V 2019 %F Adeel2019 %0 Journal Article %T Estimation of $f$-divergence and Shannon entropy by Levinson type inequalities via new Green's functions and Lidstone polynomial %A M. Adeel %A K. A. Khan %A Ð. Pečarić %A J. Pečarić %J Adv. Difference Equ. %D 2020 %V 2020 %F Adeel2020 %0 Journal Article %T Estimation of $f$-divergence and Shannon entropy by Levinson type inequalities via Fink's identity %A M. 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