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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 300–302 (Mi timm742)

On relative widths of classes of differentiable functions. III

Yu. N. Subbotinab, S. A. Telyakovskiic

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University
c Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A lower estimate is established for the minimum value of the factor $M$ for which the Kolmogorov width $d_n(W_C^r,C)$ and the relative width $K_n(W_C^r,MW_C^j,C)$ of the class of functions $W_C^r$ with respect to the class $MW^j_C$ coincide for $j>r$. The order of this estimate with respect to $n$ is the same as in the upper estimate obtained earlier.

Keywords: comparison functions, Kolmogorov and relative widths.

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UDC: 517.5

Citation: Yu. N. Subbotin, S. A. Telyakovskii, “On relative widths of classes of differentiable functions. III”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 300–302

Citation in format AMSBIB
\Bibitem{SubTel11} \by Yu.~N.~Subbotin, S.~A.~Telyakovskii \paper On relative widths of classes of differentiable functions.~III \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 3 \pages 300--302 \mathnet{http://mi.mathnet.ru/timm742} \elib{https://elibrary.ru/item.asp?id=17870142}