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

Shchitov, Alexander

doi:10.18052/www.scipress.com/IJARM.7.19

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International Journal of Advanced Research in Mathematics

IJARM Volume 7

Expansion of Function z ln z in the Quasi-Reciprocal Continued Fraction
An Investigation on an Optimal Control Problem with a Fractional Constraint in the Riemann-Liouville Sense
On Best Polynomial Approximations in the Spaces S^p and Widths of Some Classes of Functions

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On Best Polynomial Approximations in the Spaces S^p 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 S^p (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 e_n_-1(f)S^p with expressions which contain modules of continuity of functions f(x) є S^p. We have obtained the asymptotically sharp inequalities of Jackson type that connect the best polynomial approximations e_n_-1(f)S^p with modules of continuity of functions f(x) є S^p (1 ≤ p < ∞). Exact values of Kolmogorov, linear, Bernstein, Gelfand and projection n-widths in the spaces S^p are obtained for some classes of functions f(x) є S^p. 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:

https://doi.org/10.18052/www.scipress.com/IJARM.7.19

Citation:

A. Shchitov, "On Best Polynomial Approximations in the Spaces S^p and Widths of Some Classes of Functions", International Journal of Advanced Research in Mathematics, Vol. 7, pp. 19-32, 2016

Online since:

December 2016

Authors:

Alexander Shchitov

Keywords:

Best Approximations, Fourier Coefficients, Jackson's Inequality, Kolmogorov Widths, Modulus of Continuity, n-Widths, Sharp Constant, S^p Spaces, Trigonometric Polynomials

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Open Access

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Creative Commons Attribution 4.0 International License

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