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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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9404 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860956096844267520 |
|---|---|
| author | Akin, Lütfi Orhan, Hilal Akin, Lütfi Orhan, Hilal |
| author_facet | Akin, Lütfi Orhan, Hilal Akin, Lütfi Orhan, Hilal |
| author_sort | Akin, Lütfi |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-28T20:30:15Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9404 |
| first_indexed | 2026-03-29T01:00:33Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9404 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-29T01:00:33Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-94042026-03-28T20:30:15Z New developments of dynamic inequalities on time scales New developments of dynamic inequalities on time scales Akin, Lütfi Orhan, Hilal Akin, Lütfi Orhan, Hilal Time scales Hölder inequality Mean inequality Diamond alpha calculus 42B35 46N20 47A50 45P05 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. УДК 517.98 Нові результати з динамічних нерівностей на часових шкалах Встановлено нові результати для $\diamond_\alpha$-нерівностей на часових шкалах. Сформульовано динамічні нерівності типу Гільберта в $\diamond_\alpha$-численні на часових шкалах для функцій, що є $\diamond_\alpha$-диференційовними за однією та двома змінними. Отримано дискретні та неперервні нерівності як виняткові випадки наведених результатів ($\mathbb{T}=\mathbb{Z}$, $\mathbb{T}=\mathbb{R}$ і $\mathbb{T}=k\mathbb{Z}$, де $k>0$). Крім того, виведено інші нерівності на різних часових шкалах, зокрема $\mathbb{T}=q^{\mathbb{Z}}$, де $q>1$. Доведення проведено з використанням нерівності Гельдера та нерівності середнього. Institute of Mathematics, NAS of Ukraine 2026-03-28 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9404 10.3842/umzh.v78i3-4.9404 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 199–200 Український математичний журнал; Том 78 № 3-4 (2026); 199–200 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9404/10630 Copyright (c) 2026 Lütfi Akin, Hilal Orhan |
| spellingShingle | Akin, Lütfi Orhan, Hilal Akin, Lütfi Orhan, Hilal New developments of dynamic inequalities on time scales |
| title | New developments of dynamic inequalities on time scales |
| title_alt | New developments of dynamic inequalities on time scales |
| title_full | New developments of dynamic inequalities on time scales |
| title_fullStr | New developments of dynamic inequalities on time scales |
| title_full_unstemmed | New developments of dynamic inequalities on time scales |
| title_short | New developments of dynamic inequalities on time scales |
| title_sort | new developments of dynamic inequalities on time scales |
| topic_facet | Time scales Hölder inequality Mean inequality Diamond alpha calculus 42B35 46N20 47A50 45P05 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9404 |
| work_keys_str_mv | AT akinlutfi newdevelopmentsofdynamicinequalitiesontimescales AT orhanhilal newdevelopmentsofdynamicinequalitiesontimescales AT akinlutfi newdevelopmentsofdynamicinequalitiesontimescales AT orhanhilal newdevelopmentsofdynamicinequalitiesontimescales |