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Matematicheskie Zametki, 2008, Volume 84, Issue 4, Pages 583–594
DOI: https://doi.org/10.4213/mzm4103 (Mi mzm4103) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Approximation by the Class of Functions with Bounded Second Derivative

A. V. Mironenko

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (474 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4103
Abstract: The paper studies the problem of uniform approximation of a continuous function on a closed interval by the class of functions with bounded second derivative. We prove an estimate of the value of best approximation of the function by this class via its second modulus of continuity. The obtained estimate is sharp for the class of continuous functions.
Keywords: continuous function, best approximation of a function, modulus of continuity, alternance, spline, absolutely continuous function, Lipschitz function, divided difference.
Received: 16.04.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 4, Pages 544–554
DOI: https://doi.org/10.1134/S0001434608090265
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: A. V. Mironenko, “Approximation by the Class of Functions with Bounded Second Derivative”, Mat. Zametki, 84:4 (2008), 583–594; Math. Notes, 84:4 (2008), 544–554
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm4103
  • https://www.mathnet.ru/eng/mzm/v84/i4/p583
    • This publication is cited in the following 2 articles:
    1. A. V. Mironenko, “On the Jackson–Stechkin inequality for algebraic polynomials”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S116–S123  mathnet  crossref  isi  elib
    2. A. V. Mironenko, “On the estimate of the uniform deviation from the class of functions with bounded third derivative”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S168–S176  mathnet  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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