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Eurasian Math. J., 2013, Volume 4, Number 3, Pages 120–126 (Mi emj137)  

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
$$ (\int^t_0\tau\Omega^{2/m}_m(f^{(r)},\tau) d\tau)^{m/2}\le\Phi(t), $$
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.

Full text: PDF file (397 kB)
References: PDF file   HTML file
MSC: 42A10
Received: 04.10.2011
Revised: 15.06.2012
Language:

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

Citation in format AMSBIB
\Bibitem{Yus13}
\by G.~A.~Yusupov
\paper Best polynomial approximations and widths of certain classes of functions in the space~$L_2$
\jour Eurasian Math. J.
\yr 2013
\vol 4
\issue 3
\pages 120--126
\mathnet{http://mi.mathnet.ru/emj137}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet
  • Eurasian Mathematical Journal
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