Abstract
We obtain sharper estimates of the remainders in the expression for the least value of the multiplier M for which the Kolmogorov widths d n (W r C , C) and the relative widths K n (W r C ,MW j C ,C) of the class W r C with respect to the class MW j C , j < r, where r − j is odd, are equal.
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Yu. N. Subbotin and S. A. Telyakovskii, “Exact values of relative widths of classes of differentiable functions,” Mat. Zametki 65(6), 871–879 (1999) [Math. Notes 65 (5–6), 731–738 (1999)].
Yu. N. Subbotin and S. A. Telyakovskii, “On relative widths of classes of differentiable functions,” in Trudy Mat. Inst. Steklov, Vol. 248: Studies on Function Theory and Differential Equations, Collected papers dedicated to the 100th birthday of Academician S. M. Nikol’skii (Nauka, Moscow, 2005), pp. 250–261 [in Russian] [Proc. Steklov Inst.Math. 248, 243–254 (2005)].
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Original Russian Text © Yu. N. Subbotin, S. A. Telyakovskii, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 3, pp. 456–465.
An erratum to this article is available at http://dx.doi.org/10.1134/S0001434610030211.
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Subbotin, Y.N., Telyakovskii, S.A. On the equality of Kolmogorov and relative widths of classes of differentiable functions. Math Notes 86, 432 (2009). https://doi.org/10.1134/S0001434609090168
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DOI: https://doi.org/10.1134/S0001434609090168