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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1029-242X |