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.
International Journal of Advanced Research in Mathematics (Volume 7)
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