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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 622–629
DOI: https://doi.org/10.4213/mzm4610 (Mi mzm4610) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives

S. A. Telyakovskii

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (388 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm4610
Abstract: It is proved that, in the asymptotic formulas for the deviations of Bernstein polynomials from functions at the points of discontinuity of the first kind of the highest even-order derivative, the value of such a derivative can be replaced by the half-sum of its limits on the right and on the left.
Keywords: Bernstein polynomial, Peano derivative, point of discontinuity of the first kind, Stirling's formula, modulus of continuity.
Received: 14.03.2008
Revised: 22.04.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 590–596
DOI: https://doi.org/10.1134/S0001434609030304
Bibliographic databases:
Document Type: Article
UDC: 517.518.82
Language: Russian
Citation: S. A. Telyakovskii, “Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives”, Mat. Zametki, 85:4 (2009), 622–629; Math. Notes, 85:4 (2009), 590–596
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm4610
  • https://www.mathnet.ru/eng/mzm/v85/i4/p622
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    Citing articles in Google Scholar: Russian citations, English citations
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