On the approximation condition of continuity for the fractional derivative
For the space $C^\alpha$ of functions having a Marchaud continuous fractional derivative of order $\alpha>0$ on the closed interval $[0, 1]$ and for the function class $H_r [\bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(i)} (1) = 0, j = \overline {0,r} \}$ &a...
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| Дата: | 1992 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1992
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8198 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512976834920448 |
|---|---|
| author | Shakh , L. G. Шах , Л. Г. |
| author_facet | Shakh , L. G. Шах , Л. Г. |
| author_sort | Shakh , L. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-02-26T13:57:58Z |
| description | For the space $C^\alpha$ of functions having a Marchaud continuous fractional derivative of order $\alpha>0$ on the closed interval $[0, 1]$ and for the function class $H_r [\bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(i)} (1) = 0, j = \overline {0,r} \}$  it is proved that $H_r [\bar \varepsilon ]\subset C^\alpha$  if and only if  $\sum\limits_{i = 1}^\infty {\varepsilon _i j^{2\alpha - 1}< \infty }$. |
| first_indexed | 2026-03-24T03:37:21Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8198 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:37:21Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f1/f413879571aa796957b451194853aaf1.pdf |
| spelling | umjimathkievua-article-81982024-02-26T13:57:58Z On the approximation condition of continuity for the fractional derivative Об аппроксимационном условии непрерывности дробной производной Shakh , L. G. Шах , Л. Г. For the space $C^\alpha$ of functions having a Marchaud continuous fractional derivative of order $\alpha>0$ on the closed interval $[0, 1]$ and for the function class $H_r [\bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(i)} (1) = 0, j = \overline {0,r} \}$  it is proved that $H_r [\bar \varepsilon ]\subset C^\alpha$  if and only if  $\sum\limits_{i = 1}^\infty {\varepsilon _i j^{2\alpha - 1}< \infty }$. Для пространства функций $C^\alpha$, имеющих непрерывную дробную производную Маршо порядка $\alpha>0$ на отрезке $[0,1]$, и класса функций $H_r [\bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(i)} (1) = 0, j = \overline {0,r} \}$ доказано, что $H_r [\bar \varepsilon ]\subset C^\alpha$ тогда и только тогда, когда $\sum\limits_{i = 1}^\infty {\varepsilon _i j^{2\alpha - 1}< \infty }$. Для простору функцій $C^\alpha$, які мають неперервну дробову похідну Маршо порядку $\alpha>0$ на відрізку $[0,1]$, та класу функцій $H_r [\bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(i)} (1) = 0, j = \overline {0,r} \}$ доведено, що $H_r [\bar \varepsilon ]\subset C^\alpha$ тоді і тільки тоді, коли $\sum\limits_{i = 1}^\infty {\varepsilon _i j^{2\alpha - 1}< \infty }$. Institute of Mathematics, NAS of Ukraine 1992-12-04 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8198 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 12 (1992); 1719-1722 Український математичний журнал; Том 44 № 12 (1992); 1719-1722 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8198/9721 Copyright (c) 1992 L. G. Shakh |
| spellingShingle | Shakh , L. G. Шах , Л. Г. On the approximation condition of continuity for the fractional derivative |
| title | On the approximation condition of continuity for the fractional derivative |
| title_alt | Об аппроксимационном условии непрерывности дробной производной |
| title_full | On the approximation condition of continuity for the fractional derivative |
| title_fullStr | On the approximation condition of continuity for the fractional derivative |
| title_full_unstemmed | On the approximation condition of continuity for the fractional derivative |
| title_short | On the approximation condition of continuity for the fractional derivative |
| title_sort | on the approximation condition of continuity for the fractional derivative |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8198 |
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