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Eurasian Mathematical Journal, 2014, том 5, номер 1, страницы 122–134
(Mi emj152)
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Sharp inequality of Jackson–Stechkin type and widths of functional classes in the space $L_2$
M. R. Langarshoev Tadjik National University, 734025, 17 Rudaki Av., Tajikistan, Dushanbe
Аннотация:
For classes of differentiable periodic functions, defined by means of generalized moduli of continuity $\Omega_m(f,t)$, satisfying the condition
$$
\left(\int_0^h\Omega_m^{2/m}(f^{(r)},t)dt\right)\leqslant\Phi(h),
$$
where $m\in\mathbb{N}$, $r\in\mathbb{Z}_+$, $h>0$ and $\Phi$ is a given majorant, under certain restrictions on the majorant, the exact values of various $n$-widths in the space $L_2$ are calculated.
Ключевые слова и фразы:
best polynomial approximations, extremal characteristics, generalized modulus of continuity, $n$-widths.
Поступила в редакцию: 20.08.2012
Образец цитирования:
M. R. Langarshoev, “Sharp inequality of Jackson–Stechkin type and widths of functional classes in the space $L_2$”, Eurasian Math. J., 5:1 (2014), 122–134
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj152 https://www.mathnet.ru/rus/emj/v5/i1/p122
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Страница аннотации: | 182 | PDF полного текста: | 80 | Список литературы: | 46 |
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