New developments of dynamic inequalities on time scales
UDC 517.98 We establish new results for $\diamond_\alpha$-inequalities on time scales and formulate some dynamic Hilbert-type inequalities on the $\diamond_\alpha$-calculus of time scales for functions $\diamond_\alpha$-differentiable with respect to one and two variables. We obtain discrete and co...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9404 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.98
We establish new results for $\diamond_\alpha$-inequalities on time scales and formulate some dynamic Hilbert-type inequalities on the $\diamond_\alpha$-calculus of time scales for functions $\diamond_\alpha$-differentiable with respect to one and two variables. We obtain discrete and continuous inequalities as exceptional cases of our results ($\mathbb{T}=\mathbb{Z},$ $\mathbb{T}=\mathbb{R},$ and $\mathbb{T}=k\mathbb{Z},$ where $k>0$). In addition, we can derive some other inequalities on different time scales, such as $\mathbb{T}=q^{\mathbb{Z}},$ where $q>1.$ These inequalities are proved by using H\"older's inequality and the mean inequality. |
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| DOI: | 10.3842/umzh.v78i3-4.9404 |