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Problem of correctness of the best approximation in the space of continuous functions

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Abstract

Let WrH w be the subclass of those functions of Cr[a, b], for which ω(f (r),δ)⩽ω(δ), where ω(δ) is a given modulus of continuity, and Pn be the space of algebraic polynomials of degree at most n and πn(f) be the polynomial of best approximation for f(x) on [a, b]. Estimates for

and moduli of continuity of the operators of best approximation on WrH w are established. For example, if ω(δ)=δα, then

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Literature cited

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. V. Kolushov

Authors
  1. A. V. Kolushov
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Additional information

Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 351–360, March, 1978.

The author thanks S. B. Stechkin for the formulation of the problem and assistance with the article.

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Kolushov, A.V. Problem of correctness of the best approximation in the space of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 23, 190–195 (1978). https://doi.org/10.1007/BF01651430

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  • DOI: https://doi.org/10.1007/BF01651430

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