New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality

Jensen’s inequality is one of the fundamental inequalities which has several applications in almost every field of science. In 2003, Mercer gave a variant of Jensen’s inequality which is known as Jensen–Mercer’s inequality. The purpose of this article is to propose new bounds for Csiszár and related...

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Main Authors:	Muhammad Adil Khan, Zakir Husain, Yu-Ming Chu
Format:	Article
Language:	English
Published:	Hindawi-Wiley 2020-01-01
Series:	Complexity
Online Access:	http://dx.doi.org/10.1155/2020/8928691

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spelling	doaj-2188658ee06d4491ac97cbc3cbbc805f2020-11-25T04:03:29ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/89286918928691New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s InequalityMuhammad Adil Khan0Zakir Husain1Yu-Ming Chu2Department of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaJensen’s inequality is one of the fundamental inequalities which has several applications in almost every field of science. In 2003, Mercer gave a variant of Jensen’s inequality which is known as Jensen–Mercer’s inequality. The purpose of this article is to propose new bounds for Csiszár and related divergences by means of Jensen–Mercer’s inequality. Also, we investigate several new bounds for Zipf–Mandelbrot entropy. The idea of this article may further stimulate research on information theory with the help of Jensen–Mercer’s inequality.http://dx.doi.org/10.1155/2020/8928691
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Muhammad Adil Khan Zakir Husain Yu-Ming Chu
spellingShingle	Muhammad Adil Khan Zakir Husain Yu-Ming Chu New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality Complexity
author_facet	Muhammad Adil Khan Zakir Husain Yu-Ming Chu
author_sort	Muhammad Adil Khan
title	New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
title_short	New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
title_full	New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
title_fullStr	New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
title_full_unstemmed	New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
title_sort	new estimates for csiszár divergence and zipf–mandelbrot entropy via jensen–mercer’s inequality
publisher	Hindawi-Wiley
series	Complexity
issn	1076-2787 1099-0526
publishDate	2020-01-01
description	Jensen’s inequality is one of the fundamental inequalities which has several applications in almost every field of science. In 2003, Mercer gave a variant of Jensen’s inequality which is known as Jensen–Mercer’s inequality. The purpose of this article is to propose new bounds for Csiszár and related divergences by means of Jensen–Mercer’s inequality. Also, we investigate several new bounds for Zipf–Mandelbrot entropy. The idea of this article may further stimulate research on information theory with the help of Jensen–Mercer’s inequality.
url	http://dx.doi.org/10.1155/2020/8928691
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New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality

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