On Relative Widths of Classes of Differentiable Functions

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 $.