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


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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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).

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  • Continuous Function
  • Algebraic Polynomial