2018
Том 70
№ 9

# On relative widths of classes of differentiable functions. II

Abstract

We obtain an upper bound for the least value of the factor $М$ 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 $C$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 3, pp 483-493.

Citation Example: Subbotin Yu. N., Telyakovskii S. A. On relative widths of classes of differentiable functions. II // Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 423–431.

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