RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory
Abstract In the presented paper, Levinson’s inequality for 3-convex function is generalized by using two Green’s functions. Čebyšev, Grüss, and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2166-8 |
| _version_ | 1818458626806775808 |
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| author | Muhammad Adeel Khuram Ali Khan Ðilda Pečarić Josip Pečarić |
| author_facet | Muhammad Adeel Khuram Ali Khan Ðilda Pečarić Josip Pečarić |
| author_sort | Muhammad Adeel |
| collection | DOAJ |
| description | Abstract In the presented paper, Levinson’s inequality for 3-convex function is generalized by using two Green’s functions. Čebyšev, Grüss, and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via f-divergence, Rényi divergence, Rényi entropy, Shannon entropy, and Zipf–Mandelbrot law. |
| first_indexed | 2024-12-14T23:01:27Z |
| format | Article |
| id | doaj.art-d608ff228296498a93f93fae81eb0946 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-14T23:01:27Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d608ff228296498a93f93fae81eb09462022-12-21T22:44:27ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-08-012019111910.1186/s13660-019-2166-8RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theoryMuhammad Adeel0Khuram Ali Khan1Ðilda Pečarić2Josip Pečarić3Department of Mathematics, University of SargodhaDepartment of Mathematics, University of SargodhaCatholic University of Croatia, IlicaRudn UniversityAbstract In the presented paper, Levinson’s inequality for 3-convex function is generalized by using two Green’s functions. Čebyšev, Grüss, and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via f-divergence, Rényi divergence, Rényi entropy, Shannon entropy, and Zipf–Mandelbrot law.http://link.springer.com/article/10.1186/s13660-019-2166-8Levinson’s inequalityInformation theory |
| spellingShingle | Muhammad Adeel Khuram Ali Khan Ðilda Pečarić Josip Pečarić RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory Journal of Inequalities and Applications Levinson’s inequality Information theory |
| title | RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory |
| title_full | RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory |
| title_fullStr | RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory |
| title_full_unstemmed | RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory |
| title_short | RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory |
| title_sort | retracted article generalization of the levinson inequality with applications to information theory |
| topic | Levinson’s inequality Information theory |
| url | http://link.springer.com/article/10.1186/s13660-019-2166-8 |
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