On Relative Widths of Classes of Differentiable Functions

Yu. N. Subbotin ; S. A. Telyakovskii

Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 250-261

Résumé

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 $.