Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space $L_2 (R)$. II
In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness $\Lambda^w$ on the classes of functions $L^{\alpha}_2 (R)$ defined by the fractional derivatives of order $\alpha \in (0,\infty )$ in the space $L_2(R)$. The exact values of the m...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2018
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1640 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness $\Lambda^w$ on
the classes of functions $L^{\alpha}_2 (R)$ defined by the fractional derivatives of order $\alpha \in (0,\infty )$ in the space $L_2(R)$. The exact
values of the mean $\nu$ -widths for the classes of functions, defined by the generalized characteristics of smoothness $\omega w$ and
$\Lambda w$ are also computed in $L_2(R)$. |
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