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On Best Polynomial Approximations in the Spaces Sp and Widths of Some Classes of Functions

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Abstract:

In the article are studied some problems of approximation theory in the spaces Sp (1 ≤ p < ∞) introduced by A.I. Stepanets. It is obtained the exact values of extremal characteristics of a special form which connect the values of best polynomial approximations of functions en-1(f)Sp with expressions which contain modules of continuity of functions f(x) є Sp. We have obtained the asymptotically sharp inequalities of Jackson type that connect the best polynomial approximations en-1(f)Sp with modules of continuity of functions f(x) є Sp (1 ≤ p < ∞). Exact values of Kolmogorov, linear, Bernstein, Gelfand and projection n-widths in the spaces Sp are obtained for some classes of functions f(x) є Sp. The upper bound of the Fourier coefficients are found for some classes of functions.

Info:

Periodical:
International Journal of Advanced Research in Mathematics (Volume 7)
Pages:
19-32
DOI:
10.18052/www.scipress.com/IJARM.7.19
Citation:
A. N. Shchitov "On Best Polynomial Approximations in the Spaces Sp and Widths of Some Classes of Functions", International Journal of Advanced Research in Mathematics, Vol. 7, pp. 19-32, 2016
Online since:
Dec 2016
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