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Eurasian Mathematical Journal, 2013, Volume 4, Number 3, Pages 120–126
(Mi emj137)
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This article is cited in 1 scientific paper (total in 1 paper)
Best polynomial approximations and widths of certain classes of functions in the space $L_2$
G. A. Yusupov Tajik National University, 734025, Tajikistan, Dushanbe, Rudaki Av. 17
Abstract:
In the paper exact values of the $n$-widths are found for the class of differentiable periodic functions in the space $L_2[0,2\pi]$, satisfying the condition
$$
\left(\int^t_0\tau\Omega^{2/m}_m(f^{(r)},\tau)\,d\tau\right)^{m/2}\le\Phi(t),
$$
where $0<t\le\pi/n$, $m,n,r\in\mathbb N$, $\Omega_m(f^{(r)},\tau)$ is the generalized modulus of continuity of order $m$ of the derivative $f^{(r)}\in L_2[0,2\pi]$, and $\Phi(t)$, $0\le t<\infty$ is a continuous non-decreasing function, such that $\Phi(0)=0$ and $\Phi(t)>0$ for $t>0$.
Keywords and phrases:
best polynomial approximations, generalized modulus of continuity, extremal characteristics, widths.
Received: 04.10.2011 Revised: 15.06.2012
Citation:
G. A. Yusupov, “Best polynomial approximations and widths of certain classes of functions in the space $L_2$”, Eurasian Math. J., 4:3 (2013), 120–126
Linking options:
https://www.mathnet.ru/eng/emj137 https://www.mathnet.ru/eng/emj/v4/i3/p120
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Abstract page: | 228 | Full-text PDF : | 67 | References: | 41 |
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