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Sibirsk. Mat. Zh., 2011, Volume 52, Number 6, Pages 1414–1427 (Mi smj2284)  

This article is cited in 5 scientific papers (total in 5 papers)

Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$

M. Sh. Shabozova, G. A. Yusupovb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe, Tajikistan
b Tajik National University, Dushanbe, Tajikistan

Abstract: We find the exact values of the $n$-widths for the classes of periodic differentiable functions in $L_2[0,2\pi]$, satisfying the constraint
$$ \int_0^ht\widetilde\Omega_m^{1/m}(f^{(r)};t) dt\le\Phi(h), $$
where $h>0$, $m\in\mathbb N$, $r\in\mathbb Z_+$, $\widetilde\Omega_m^{1/m}(f^{(r)};t)$ is the generalized $m$th order continuity modulus of the derivative $f^{(r)}\in L_2[0,2\pi]$, while $\Phi(t)$ is an arbitrary increasing function such that $\Phi(0)=0$.

Keywords: space of square integrable functions, best approximation, extremal characteristic, generalized continuity modulus, width.

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English version:
Siberian Mathematical Journal, 2011, 52:6, 1124–1136

Bibliographic databases:

UDC: 517.5
Received: 11.01.2011
Revised: 10.05.2011

Citation: M. Sh. Shabozov, G. A. Yusupov, “Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$”, Sibirsk. Mat. Zh., 52:6 (2011), 1414–1427; Siberian Math. J., 52:6 (2011), 1124–1136

Citation in format AMSBIB
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\by M.~Sh.~Shabozov, G.~A.~Yusupov
\paper Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in~$L_2$
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 6
\pages 1414--1427
\mathnet{http://mi.mathnet.ru/smj2284}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2961765}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 6
\pages 1124--1136
\crossref{https://doi.org/10.1134/S0037446611060176}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855170740}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. Tukhliev, “O priblizhenii periodicheskikh funktsii v $L_2$ i znacheniyakh poperechnikov nekotorykh klassov funktsii”, Model. i analiz inform. sistem, 22:1 (2015), 127–143  mathnet  mathscinet  elib
    2. S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Math. Notes, 98:4 (2015), 572–588  mathnet  crossref  crossref  mathscinet  isi  elib
    3. S. B. Vakarchuk, V. I. Zabutnaya, “Inequalities between Best Polynomial Approximations and Some Smoothness Characteristics in the Space $L_2$ and Widths of Classes of Functions”, Math. Notes, 99:2 (2016), 222–242  mathnet  crossref  crossref  mathscinet  isi  elib
    4. K. Tukhliev, “Nailuchshie priblizheniya i poperechniki nekotorykh klassov svertok v $L_{2}$”, Tr. IMM UrO RAN, 22, no. 4, 2016, 284–294  mathnet  crossref  mathscinet  elib
    5. S. B. Vakarchuk, “Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths for the classes of $(\psi, \beta)$-differentiable functions in $L_2$. I”, Ukr. Math. J., 68:6 (2016), 823–848  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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