Several Jensen–Grüss inequalities with applications in information theory
UDC 517.5 Several integral Jensen–Grüss  inequalities are proved together with their refinements.  Some new bounds for integral Jensen–Chebyshev  inequality are obtained. The multidimensional integral variants are also pre...
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| Date: | 2023 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6554 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
Several integral Jensen–Grüss  inequalities are proved together with their refinements.  Some new bounds for integral Jensen–Chebyshev  inequality are obtained. The multidimensional integral variants are also presented.  In addition, some integral Jensen–Grüss  inequalities for monotone  and completely monotone functions are established.  Finally, as an application, we present the refinements  for Shannon's entropy. |
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| DOI: | 10.37863/umzh.v74i12.6554 |