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Matematicheskie Zametki, 1972, Volume 12, Issue 6, Pages 701–712 (Mi mzm9935)  
The simultaneous interpolation and one-sided approximation in the mean of continuous functions

V. A. Shmatkov

Moscow Technological Institute of the Food Industry
Full-text PDF (1214 kB)
Abstract: We consider the best one-sided approximation in the mean of a continuous function with simultaneous interpolation of this function by Chebyshev polynomials. It is proved that the polynomial of best approximation for this problem is unique in the case when the Chebyshev system is differentiable three times and the function being approximated has a continuous third-order derivative. It is shown that the conditions imposed are essential.
Received: 24.12.1971
English version:
Mathematical Notes, 1972, Volume 12, Issue 6, Pages 861–867
DOI: https://doi.org/10.1007/BF01156045
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. A. Shmatkov, “The simultaneous interpolation and one-sided approximation in the mean of continuous functions”, Mat. Zametki, 12:6 (1972), 701–712; Math. Notes, 12:6 (1972), 861–867
Citation in format AMSBIB
\Bibitem{Shm72}
\by V.~A.~Shmatkov
\paper The simultaneous interpolation and one-sided approximation in the mean of continuous functions
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 6
\pages 701--712
\mathnet{http://mi.mathnet.ru/mzm9935}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=318730}
\zmath{https://zbmath.org/?q=an:0246.41013}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 6
\pages 861--867
\crossref{https://doi.org/10.1007/BF01156045}
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