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Matematicheskie Trudy, 2015, Volume 18, Number 2, Pages 22–38
DOI: https://doi.org/10.17377/mattrudy.2015.18.202 (Mi mt291) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On partial derivatives of multivariate Bernstein polynomials

A. Yu. Veretennikovabc, E. V. Veretennikovad

a Institute for Information Transmission Problems, Russian Academy of Sciences
b University of Leeds
c National Research University "Higher School of Economics" (HSE), Moscow
d Moscow Pedagogical University, Moscow, Russian Federation, Moscow
Full-text PDF (231 kB) Citations (9)
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DOI: https://doi.org/10.17377/mattrudy.2015.18.202
Abstract: It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus.
Key words: multivariate Bernstein polynomial, partial derivative, convergence.
Funding agency Grant number
National Research University Higher School of Economics
Received: 10.10.2014
English version:
Siberian Advances in Mathematics, 2016, Volume 26, Issue 4, Pages 294–305
DOI: https://doi.org/10.3103/S1055134416040039
Bibliographic databases:
Document Type: Article
UDC: 519.21:519.65:517.518.8
Language: Russian
Citation: A. Yu. Veretennikov, E. V. Veretennikova, “On partial derivatives of multivariate Bernstein polynomials”, Mat. Tr., 18:2 (2015), 22–38; Siberian Adv. Math., 26:4 (2016), 294–305
Citation in format AMSBIB
\Bibitem{VerVer15}
\by A.~Yu.~Veretennikov, E.~V.~Veretennikova
\paper On partial derivatives of multivariate Bernstein polynomials
\jour Mat. Tr.
\yr 2015
\vol 18
\issue 2
\pages 22--38
\mathnet{http://mi.mathnet.ru/mt291}
\crossref{https://doi.org/10.17377/mattrudy.2015.18.202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588289}
\elib{https://elibrary.ru/item.asp?id=24639777}
\transl
\jour Siberian Adv. Math.
\yr 2016
\vol 26
\issue 4
\pages 294--305
\crossref{https://doi.org/10.3103/S1055134416040039}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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