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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 292–308 (Mi timm1251)  

This article is cited in 3 scientific papers (total in 3 papers)

Jackson — Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions

M. Sh. Shabozova, K.Tukhlievb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
b Khujand State University

Abstract: In the Hilbert space $L_{2,\mu}[-1,1]$ with Chebyshev weight $\mu(x):=1/\sqrt{1-x^{2}}$, we obtain Jackson–Stechkin type inequalities between the value $E_{n-1}(f)_{L_{2,\mu}}$ of the best approximation of a function $f(x)$ by algebraic polynomials of degree at most $n-1$ and the $m$th-order generalized modulus of continuity $\Omega_{m}({\mathcal D}^{r}f;t)$, where ${\mathcal D}$ is some second-order differential operator. For classes of functions $W^{(2r)}_{p,m}(\Psi)$ ($m,r\in\mathbb{N}$, $1/(2r)$<$p\le2$) defined by the mentioned modulus of continuity and a given majorant $\Psi(t)$ ($t\ge0$), which satisfies certain constraints, we calculate the values of various $n$-widths in the space $L_{2,\mu}[-1,1]$.

Keywords: best approximation, Chebyshev polynomials, generalized modulus of continuity of $m$th order, Chebyshev — Fourier coefficients, $n$-widths.

Full text: PDF file (237 kB)
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Bibliographic databases:
UDC: 517.5
Received: 27.05.2014

Citation: M. Sh. Shabozov, K.Tukhliev, “Jackson — Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 292–308

Citation in format AMSBIB
\Bibitem{ShaTuk15}
\by M.~Sh.~Shabozov, K.Tukhliev
\paper Jackson --- Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 4
\pages 292--308
\mathnet{http://mi.mathnet.ru/timm1251}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468452}
\elib{http://elibrary.ru/item.asp?id=25301007}


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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. K. Tukhliev, “Srednekvadraticheskoe priblizhenie funktsii ryadami Fure–Besselya i znacheniya poperechnikov nekotorykh funktsionalnykh klassov”, Chebyshevskii sb., 17:4 (2016), 141–156  mathnet  crossref  elib
    2. Mukim S. Saidusajnov, “$\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space”, Ural Math. J., 3:2 (2017), 74–81  mathnet  crossref  mathscinet
    3. M. Sh. Shabozov, M. S. Saidusajnov, “Upper Bounds for the Approximation of Certain Classes of Functions of a Complex Variable by Fourier Series in the Space $L_2$ and $n$-Widths”, Math. Notes, 103:4 (2018), 656–668  mathnet  crossref  crossref  isi  elib
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