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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 289–296 (Mi tm600)  
This article is cited in 7 scientific papers (total in 7 papers)

On the Approximation of Differentiable Functions by Bernstein Polynomials and Kantorovich Polynomials

S. A. Telyakovskii

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (147 kB) Citations (7)
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Abstract: E. V. Voronovskaya and S. N. Bernstein established an asymptotic representation for the deviation of functions from Bernstein polynomials under the condition that the function has an even-order derivative. In the present paper, a similar problem is solved in the case when the function has an odd-order derivative. In addition, analogous representations are obtained for the deviations of functions from Kantorovich polynomials.
Received in June 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 260, Pages 279–286
DOI: https://doi.org/10.1134/S0081543808010197
Bibliographic databases:
Document Type: Article
UDC: 517.518.82
Language: Russian
Citation: S. A. Telyakovskii, “On the Approximation of Differentiable Functions by Bernstein Polynomials and Kantorovich Polynomials”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 289–296; Proc. Steklov Inst. Math., 260 (2008), 279–286
Citation in format AMSBIB
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\paper On the Approximation of Differentiable Functions by Bernstein Polynomials and Kantorovich Polynomials
\inbook Function theory and nonlinear partial differential equations
\bookinfo Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday
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\pages 289--296
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm600
  • https://www.mathnet.ru/eng/tm/v260/p289
    • This publication is cited in the following 7 articles:
    1. I. V. Okorochkov, I. V. Tikhonov, V. B. Sherstyukov, “On a Connection of Bernstein and Kantorovich Polynomials for a Symmetric Modulus Function”, Sib Math J, 64:3 (2023), 747  crossref
    2. I. V. Okorochkov, I. V. Tikhonov, V. B. Sherstyukov, “O svyazi polinomov Bernshteina i Kantorovicha dlya simmetrichnogo modulya”, Vladikavk. matem. zhurn., 24:1 (2022), 87–99  mathnet  crossref  mathscinet
    3. Tikhonov I.V., Sherstyukov V.B., “Priblizhenie modulya polinomami Bernshteina”, Vestnik chelyabinskogo gosudarstvennogo universiteta, 2012, no. 26, 6–40  elib
    4. I. V. Tikhonov, V. B. Sherstyukov, “Priblizhenie modulya polinomami Bernshteina”, Vestnik ChelGU, 2012, no. 15, 6–40  mathnet
    5. V. O. Tonkov, “Approximation by Bernstein polynomials at the discontinuity points of derivatives”, Proc. Steklov Inst. Math., 269 (2010), 259–264  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. S. A. Telyakovskii, “Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives”, Math. Notes, 85:4 (2009), 590–596  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. S. A. Telyakovskii, “On the rate of approximation of functions by the Bernstein polynomials”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S177–S184  mathnet  crossref  isi  elib
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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