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Matematicheskie Zametki, 1978, Volume 23, Issue 5, Pages 659–669 (Mi mzm9995)  
This article is cited in 9 scientific papers (total in 9 papers)

Certain positive linear operators

Yu. I. Volkov

Vinnitsa Polytechnic Institute
Full-text PDF (878 kB) Citations (9)
Abstract: Properties (including the approximating ones) are investigated of positive linear operators $L_n(f; x)$ for which the relation
$$ L_n((t-x)f(t);x)=\frac{\varphi(x)}{n}L_n'(f(t); x) $$
is fulfilled, as well as the properties of operators $L_n^{(m)}(f; x)$. The results are applicable, in particular, to Bernstein polynomials, to the operators of Mirak'yan, Baskakov, and others.
Received: 24.01.1977
English version:
Mathematical Notes, 1978, Volume 23, Issue 5, Pages 363–368
DOI: https://doi.org/10.1007/BF01789002
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: Yu. I. Volkov, “Certain positive linear operators”, Mat. Zametki, 23:5 (1978), 659–669; Math. Notes, 23:5 (1978), 363–368
Citation in format AMSBIB
\Bibitem{Vol78}
\by Yu.~I.~Volkov
\paper Certain positive linear operators
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 5
\pages 659--669
\mathnet{http://mi.mathnet.ru/mzm9995}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=493086}
\zmath{https://zbmath.org/?q=an:0408.41009|0385.41016}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 5
\pages 363--368
\crossref{https://doi.org/10.1007/BF01789002}
Linking options:
  • https://www.mathnet.ru/eng/mzm9995
  • https://www.mathnet.ru/eng/mzm/v23/i5/p659
    • This publication is cited in the following 9 articles:
    1. Adrian Holhoş, “A Voronovskaya-type theorem in simultaneous approximation”, Period Math Hung, 85:2 (2022), 280  crossref
    2. Adrian Holhoş, “Voronovskaya-type Results for Positive Linear Operators of Exponential Type and their Derivatives”, Bull. Malays. Math. Sci. Soc., 45:4 (2022), 1839  crossref
    3. Jorge Bustamante, Bernstein Operators and Their Properties, 2017, 75  crossref
    4. Yu. I. Volkov, “Generalized Bezier Transformation”, Math. Notes, 97:5 (2015), 669–678  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Jorge Bustamante, Abisaí Carrillo-Zentella, José M. Quesada, “Direct and strong converse theorems for a general sequence of positive linear operators”, Acta Math Hung, 136:1-2 (2012), 90  crossref
    6. T. V. Ershova, “Asymptotics for central moments of modifications of operators similar to Bernstein polynomials”, Russian Math. (Iz. VUZ), 47:9 (2003), 8–14  mathnet  mathscinet  zmath
    7. T. V. Ershova, “Asymptotic theorems for modifications of polynomials similar to Bernstein polynomials”, Russian Math. (Iz. VUZ), 44:9 (2000), 7–13  mathnet  mathscinet  zmath
    8. T. V. Ershova, “Asimptoticheskaya teorema Voronovskoi-Bernshteina dlya modifikatsii mnogochlenov Bernshteina”, Vestnik ChelGU, 1994, no. 2, 43–48  mathnet  zmath
    9. Yu. I. Volkov, “Multidimensional approximation operators generated by Lebesgue–Stieltjes measures”, Math. USSR-Izv., 22:3 (1984), 399–418  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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