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
Publication Date: May 15, 2020 Submission Date: October 12, 2019 Revision Date: February 07, 2020 Accteptance Date: March 13, 2020
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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

Keywords

• Information theory
• convex functions
• Levinson's inequality

•  94A15
•  94A17
•  26D15

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