This article is cited in 6 papers

On 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
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The Kolmogorov widths $d_{2n} (W^r_C, C)$ and relative widths $K_{2n}(W^r_C,MW^j_C,C)$ of the class $W^r_C$ with respect to $MW^j_C$, where $j < r$, are considered. The minimal multiplier $M$ for which these widths are equal is estimated from above and below; the bounds obtained show that this minimal value is asymptotically equal to the Favard constant $\mathcal K_{r-j}$ as $n \to \infty $.

UDC: 517.224

Received in September 2004

 English version: Proceedings of the Steklov Institute of Mathematics, 2005, 248, 243–254

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