This article is cited in 4 papers

Sharpening of the estimates for relative widths of classes of differentiable functions

Yu. N. Subbotin^a, S. A. Telyakovskii<sup>b

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
^b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We improve the earlier obtained upper estimates for the least value of the coefficient $M$ for which the Kolmogorov widths $d_n(W_C^r,C)$ of the function class $W_C^r$ are equal to the relative widths $K_n(W_C^r,MW_C^j,C)$ of the class $W_C^r$ with respect to the class $MW_C^j$, $j<r$.

UDC: 517.518.224

Received in October 2009

 English version: Proceedings of the Steklov Institute of Mathematics, 2010, 269, 235–246

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