Estimation of f-divergence and Shannon entropy by Bullen type inequalities via Fink’s identity-Reference-Cited by-同舟云学术

Estimation of f-divergence and Shannon entropy by Bullen type inequalities via Fink’s identity

Published:2022 Issue:2 Volume:36 Page:527-538
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Adeel Muhammad¹,Khan Khuram²,Pecaric Ðilda³,Pecaric Josip⁴

Affiliation:

1. Department of Mathematics, University of Sargodha, Sargodha, Pakistan + University of central Punjab, Lahore, Pakistan

2. Department of Mathematics, University of Sargodha, Sargodha, Pakistan

3. University North, Koprivnica, Croatia

4. Croatian Academy of Sciences and Arts, Zagreb, Croatia

Abstract

By using Fink?s identity some new generalizations of Levinson type inequalities for n-convex functions are obtained. 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.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference25 articles.

1. J. Pečarić, F. Proschan and Y. L. Tong, Convex functions, Partial Orderings and Statistical Applications, Academic Press, New York, (1992).

2. A. M. Fink, Bounds of the deviation of a function from its avereges, Czechoslovak Math. J. 42, (117) 289--310 (1992).

3. S. I. Butt, K. A. Khan, J. Pecaric, Generaliztion of Popoviciu inequality for higher order convex function via Tayor’s polynomial, Acta Univ. Apulensis Math. Inform, 42, 181-200, (2015).

4. G. Aras-Gazić, V. Culjak, J. Pečarić, A. Vukelić, Generalization of Jensen’s inequality by Lidstone’s polynomial and related results, Math. Inequal. Appl. 164, 1243-1267, (2013).

5. M. Adeel, K. A. Khan, Ð. Pečarić and J. Pečarić, Generalization of the Levinson inequality with applications to information theorey, J. Inequal. Appl., 230(2019).

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Generalizations of Levinson-type inequalities via new Green functions and Hermite interpolating polynomial;Journal of Inequalities and Applications;2024-05-17

2. Generalizations of Levinson type inequalities via new Green functions with applications to information theory;Journal of Inequalities and Applications;2023-10-02