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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8928691 |
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| _version_ | 1832546995014729728 |
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| author | Muhammad Adil Khan Zakir Husain Yu-Ming Chu |
| author_facet | Muhammad Adil Khan Zakir Husain Yu-Ming Chu |
| author_sort | Muhammad Adil Khan |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-2188658ee06d4491ac97cbc3cbbc805f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2188658ee06d4491ac97cbc3cbbc805f2025-02-03T06:46:21ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/89286918928691New 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 |
| spellingShingle | Muhammad Adil Khan Zakir Husain Yu-Ming Chu New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality Complexity |
| title | 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_short | New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality |
| title_sort | new estimates for csiszar divergence and zipf mandelbrot entropy via jensen mercer s inequality |
| url | http://dx.doi.org/10.1155/2020/8928691 |
| work_keys_str_mv | AT muhammadadilkhan newestimatesforcsiszardivergenceandzipfmandelbrotentropyviajensenmercersinequality AT zakirhusain newestimatesforcsiszardivergenceandzipfmandelbrotentropyviajensenmercersinequality AT yumingchu newestimatesforcsiszardivergenceandzipfmandelbrotentropyviajensenmercersinequality |