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Mat. Zametki, 1972, Volume 12, Issue 6, Pages 701–712 (Mi mz9935)  

The simultaneous interpolation and one-sided approximation in the mean of continuous functions

V. A. Shmatkov

Moscow Technological Institute of the Food Industry

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.

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English version:
Mathematical Notes, 1972, 12:6, 861–867

Bibliographic databases:

UDC: 517.5
Received: 24.12.1971

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/mz9935}
\mathscinet{http://www.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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