Generalizations of Shannon type inequalities via diamond integrals on time scales
Abstract The paper generalizes Shannon-type inequalities for diamond integrals. It includes two-dimensional Hölder’s inequality and Cauchy–Schwartz’s inequality, which help to prove weighted Grüss’s inequality for diamond integrals. Jensen’s inequality and Grüss’s inequality are used to provide Shan...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02930-4 |
| _version_ | 1811165652476493824 |
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| author | Muhammad Bilal Khuram Ali Khan Ammara Nosheen Josip Pečarić |
| author_facet | Muhammad Bilal Khuram Ali Khan Ammara Nosheen Josip Pečarić |
| author_sort | Muhammad Bilal |
| collection | DOAJ |
| description | Abstract The paper generalizes Shannon-type inequalities for diamond integrals. It includes two-dimensional Hölder’s inequality and Cauchy–Schwartz’s inequality, which help to prove weighted Grüss’s inequality for diamond integrals. Jensen’s inequality and Grüss’s inequality are used to provide Shannon-type inequalities for diamond integrals. Shannon-type inequalities for multiple integrals are also part of the discussion. Moreover, many distributions are deduced from the main results, and new bounds are obtained. |
| first_indexed | 2024-04-10T15:41:17Z |
| format | Article |
| id | doaj.art-b276e1732d4143e783dd3e140d2e4ce5 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-10T15:41:17Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-b276e1732d4143e783dd3e140d2e4ce52023-02-12T12:25:47ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-02-012023111910.1186/s13660-023-02930-4Generalizations of Shannon type inequalities via diamond integrals on time scalesMuhammad Bilal0Khuram Ali Khan1Ammara Nosheen2Josip Pečarić3Department of Mathematics, University of SargodhaDepartment of Mathematics, University of SargodhaDepartment of Mathematics, University of SargodhaCroatian Academy of Science and Arts HRAbstract The paper generalizes Shannon-type inequalities for diamond integrals. It includes two-dimensional Hölder’s inequality and Cauchy–Schwartz’s inequality, which help to prove weighted Grüss’s inequality for diamond integrals. Jensen’s inequality and Grüss’s inequality are used to provide Shannon-type inequalities for diamond integrals. Shannon-type inequalities for multiple integrals are also part of the discussion. Moreover, many distributions are deduced from the main results, and new bounds are obtained.https://doi.org/10.1186/s13660-023-02930-4Shannon entropyDiamond integralInformation theory |
| spellingShingle | Muhammad Bilal Khuram Ali Khan Ammara Nosheen Josip Pečarić Generalizations of Shannon type inequalities via diamond integrals on time scales Journal of Inequalities and Applications Shannon entropy Diamond integral Information theory |
| title | Generalizations of Shannon type inequalities via diamond integrals on time scales |
| title_full | Generalizations of Shannon type inequalities via diamond integrals on time scales |
| title_fullStr | Generalizations of Shannon type inequalities via diamond integrals on time scales |
| title_full_unstemmed | Generalizations of Shannon type inequalities via diamond integrals on time scales |
| title_short | Generalizations of Shannon type inequalities via diamond integrals on time scales |
| title_sort | generalizations of shannon type inequalities via diamond integrals on time scales |
| topic | Shannon entropy Diamond integral Information theory |
| url | https://doi.org/10.1186/s13660-023-02930-4 |
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