We obtain an upper bound for the least value of the factor M for which the Kolmogorov widths d n (W C r, C) are equal to the relative widths K n (W C r, MW C j, C) of the class of functions W C r with respect to the class MW C j, provided that j > r. This estimate is also true in the case where the space L is considered instead of C.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 423–431, March, 2010.
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Subbotin, Y.N., Telyakovskii, S.A. On relative widths of classes of differentiable functions. II. Ukr Math J 62, 483–493 (2010). https://doi.org/10.1007/s11253-010-0365-z
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DOI: https://doi.org/10.1007/s11253-010-0365-z