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

Volume 21, Issue 4, pp 322--334 http://dx.doi.org/10.22436/jmcs.021.04.05
Publication Date: May 15, 2020 Submission Date: October 12, 2019 Revision Date: February 07, 2020 Accteptance Date: March 13, 2020

Authors

Muhammad Adeel - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. - Department of Mathematics, University of Central Punjab, Lahore, Pakistan. Khuram Ali Khan - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. Ðilda Pečarić - University of Croatia, Ilica 242, Zagreb, Croatia. Josip Pečarić - RUDN University, Moscow, Russia.


Abstract

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.


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ISRP Style

Muhammad Adeel, Khuram Ali Khan, Ðilda Pečarić, Josip Pečarić, Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial, Journal of Mathematics and Computer Science, 21 (2020), no. 4, 322--334

AMA Style

Adeel Muhammad, Khan Khuram Ali, Pečarić Ðilda, Pečarić Josip, Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial. J Math Comput SCI-JM. (2020); 21(4):322--334

Chicago/Turabian Style

Adeel, Muhammad, Khan, Khuram Ali, Pečarić, Ðilda, Pečarić, Josip. "Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial." Journal of Mathematics and Computer Science, 21, no. 4 (2020): 322--334


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