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Mat. Zametki, 2009, Volume 85, Issue 3, Pages 323–329 (Mi mz6633)  

This article is cited in 8 scientific papers (total in 8 papers)

Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$

S. B. Vakarchuka, V. I. Zabutnayab

a Ukrainian Academy of Customs
b Dnepropetrovsk National University

Abstract: In the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$, we construct best linear approximation methods for classes of analytic functions $W^rH_q\Phi$, $r\in\mathbb N$, in the unit disk (studied by L. V. Taikov) whose averaged second-order moduli of continuity of the angular boundary values of the $r$th derivatives are majorized by a given function $\Phi$ satisfying certain constraints.

Keywords: linear approximation of functions, analytic function, Hardy spaces $H_{q,\rho}$, modulus of continuity, $n$-width (Bernstein, Kolmogorov, Gelfand), algebraic polynomial, Minkowski's inequality

DOI: https://doi.org/10.4213/mzm6633

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English version:
Mathematical Notes, 2009, 85:3, 322–327

Bibliographic databases:

UDC: 517.5
Received: 18.12.2001
Revised: 08.10.2008

Citation: S. B. Vakarchuk, V. I. Zabutnaya, “Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$”, Mat. Zametki, 85:3 (2009), 323–329; Math. Notes, 85:3 (2009), 322–327

Citation in format AMSBIB
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\paper Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 3
\pages 323--329
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2548040}
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\pages 322--327
\crossref{https://doi.org/10.1134/S000143460903002X}
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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. Vakarchuk S.B., Shabozov M.Sh., “On widths of classes of analytic functions on the disk in weight Banach spaces”, Dokl. Math., 81:3 (2010), 426–428  crossref  mathscinet  zmath  isi  elib  scopus
    2. Vakarchuk S.B. Vakarchuk M.B., “Inequalities of Kolmogorov type for analytic functions of one and two complex variables and their applications to approximation theory”, Ukr. Math. J., 63:12 (2012), 1795–1819  crossref  zmath  isi  scopus
    3. Yusupov G.A., Mirkalonova M.M., “O poperechnikakh nekotorykh klassov analiticheskikh v edinichnom kruge funktsii”, Doklady Akademii nauk Respubliki Tadzhikistan, 56:11 (2013), 869–876  elib
    4. Yusupov G.A., “O nailuchshikh lineinykh metodakh priblizheniya funktsii v prostranstvakh Khardi $H_{q,R}, $0<R<1$”, Doklady Akademii nauk Respubliki Tadzhikistan, 56:12 (2013), 946–953  elib
    5. M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$”, Siberian Math. J., 57:2 (2016), 369–376  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Langarshoev M.R., “On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space”, Ukr. Math. J., 67:10 (2016), 1537–1551  crossref  mathscinet  zmath  isi  elib  scopus
    7. M. R. Langarshoev, “O nailuchshem polinomialnom priblizhenii funktsii v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 21:1 (2019), 27–36  mathnet  crossref
    8. M. Sh. Shabozov, M. R. Langarshoev, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh v edinichnom kruge funktsii”, Sib. matem. zhurn., 60:6 (2019), 1414–1423  mathnet  crossref
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