Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$
We continue the investigation of approximation properties of the space $S^p$. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space $S^p$ in terms of the best approximations and moduli of continuity. These theorems are analogous...
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| Дата: | 2002 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2002
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4044 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510174593155072 |
|---|---|
| author | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. |
| author_facet | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. |
| author_sort | Serdyuk, A. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:16Z |
| description | We continue the investigation of approximation properties of the space $S^p$. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space $S^p$ in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein. |
| first_indexed | 2026-03-24T02:52:48Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4044 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:48Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ee/0ec8cd85736d54454140eba8d4c238ee.pdf |
| spelling | umjimathkievua-article-40442020-03-18T20:20:16Z Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ Прямые и обратные теоремы теории приближения функций в пространстве $S^p$ Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. We continue the investigation of approximation properties of the space $S^p$. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space $S^p$ in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein. Продовжується вивчення апроксимаційних властивостей простору Sp. Вводиться поняття $k$- го модуля неперервності та доводяться прямі й обернені теореми наближення в просторі $S^p$ у термінах найкращих наближень і модулів неперервності, подібні до відомих теорем Д. Джексона та С. Н. Бернштейна. Institute of Mathematics, NAS of Ukraine 2002-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4044 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 1 (2002); 106-124 Український математичний журнал; Том 54 № 1 (2002); 106-124 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4044/4798 https://umj.imath.kiev.ua/index.php/umj/article/view/4044/4799 Copyright (c) 2002 Serdyuk A. S.; Stepanets O. I. |
| spellingShingle | Serdyuk, A. S. Stepanets, O. I. Сердюк, А. С. Степанец, А. И. Сердюк, А. С. Степанец, А. И. Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title | Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title_alt | Прямые и обратные теоремы теории приближения
функций в пространстве $S^p$ |
| title_full | Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title_fullStr | Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title_full_unstemmed | Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title_short | Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ |
| title_sort | direct and inverse theorems in the theory of approximation of functions in the space $s^p$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4044 |
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