Generalization of the Levinson inequality with applications to information theory
Abstract In the presented paper, Levinson’s inequality for the 3-convex function is generalized by using two Green 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...
| 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/s13660-019-2186-4 |
| _version_ | 1818113032234991616 |
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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 the 3-convex function is generalized by using two Green 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 the f-divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf–Mandelbrot law. |
| first_indexed | 2024-12-11T03:28:23Z |
| format | Article |
| id | doaj.art-11998a28c2ec4bc793bdcb7a8495ab20 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T03:28:23Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-11998a28c2ec4bc793bdcb7a8495ab202022-12-22T01:22:27ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-08-012019111810.1186/s13660-019-2186-4Generalization 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 the 3-convex function is generalized by using two Green 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 the f-divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf–Mandelbrot law.http://link.springer.com/article/10.1186/s13660-019-2186-4Levinson’s inequalityInformation theory |
| spellingShingle | Muhammad Adeel Khuram Ali Khan Ðilda Pečarić Josip Pečarić Generalization of the Levinson inequality with applications to information theory Journal of Inequalities and Applications Levinson’s inequality Information theory |
| title | Generalization of the Levinson inequality with applications to information theory |
| title_full | Generalization of the Levinson inequality with applications to information theory |
| title_fullStr | Generalization of the Levinson inequality with applications to information theory |
| title_full_unstemmed | Generalization of the Levinson inequality with applications to information theory |
| title_short | Generalization of the Levinson inequality with applications to information theory |
| title_sort | generalization of the levinson inequality with applications to information theory |
| topic | Levinson’s inequality Information theory |
| url | http://link.springer.com/article/10.1186/s13660-019-2186-4 |
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