On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions

We obtain sharper estimates of the remainders in the expression for the least value of the multiplier $M$ for which the Kolmogorov widths $d_n(W_C^r,C)$ and the relative widths $K_n(W_C^r,MW_C^j,C)$ of the class $W_C^r$ with respect to the class $MW_C^j$, $j<r$, where $r-j$ is odd, are equal.