We consider the problem of the best polynomial approximation of 2π-periodic functions in the space L 2 in the case where the error of approximation E n−1(f) is estimated via the kth-order modulus of continuity Ω k (f) in which the Steklov operator S h f is used instead of the operator of translation T h f(x) = f(x + h). For the classes of functions defined by using the indicated characteristic of smoothness, we determine the exact values of various n-widths.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 8, pp. 1025–1032, August, 2012.
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Vakarchuk, S.B., Zabutnaya, V.I. On the best polynomial approximation in the space L 2 and widths of some classes of functions. Ukr Math J 64, 1168–1176 (2013). https://doi.org/10.1007/s11253-013-0707-8
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DOI: https://doi.org/10.1007/s11253-013-0707-8