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

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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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Authors and Affiliations

  1. Moscow Technological Institute of the Food Industry, USSR

    V. A. Shmatkov

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  1. V. A. Shmatkov
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Translated from Matematicheskie Zametki, Vol. 12, No. 6, pp. 701–712, December, 1972.

The author wishes to use this occasion to express his deep gratitude to A. L. Garkavi for formulating the problem and for useful advice.

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Shmatkov, V.A. The simultaneous interpolation and one-sided approximation in the mean of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 12, 861–867 (1972). https://doi.org/10.1007/BF01156045

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  • DOI: https://doi.org/10.1007/BF01156045

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