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This article is cited in 4 scientific papers (total in 4 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.
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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{https://elibrary.ru/item.asp?id=25301007}
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Mukim S. Saidusajnov, “$\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space”, Ural Math. J., 3:2 (2017), 74–81
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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
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O. A. Dzhurakhonov, “Priblizhenie funktsii dvukh peremennykh «krugovymi»
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