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