Problem of correctness of the best approximation in the space of continuous functions |
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Authors: | A V Kolushov |
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Institution: | (1) M. V. Lomonosov Moscow State University, USSR |
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Abstract: | Let WrH
w
be the subclass of those functions of Cra, b], for which (f
(r),)(), where () is a given modulus of continuity, and Pn be the space of algebraic polynomials of degree at most n and n(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 ()=, then
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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Keywords: | |
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