Best methods of approximation and interpolation of differentiable functions in the space $C_{[-1,1]}$

In this paper are computed the $n$-diameter of the class
$$ W_r=\{f(x):|f^{(r-1)}(x)-f^{(r-1)}(x')|\leqslant|x-x'|,|x|,|x'|\leqslant1\} $$
of functions defined on $[-1,1]$ in $C_{[-1,1]}$.
This problem reduces to the variational problem
\begin{gather*} \lambda_{nr}=\inf||x||,\\ x^{(r+1)}=2\sum_{k=1}^m(-1)^{k+1}\delta(t-t_k),\qquad-1\leqslant t_1\leqslant\dots\leqslant t_m\leqslant1,\quad m\leqslant n,\\ x^r(t)\equiv-1,\qquad t\leqslant-1, \end{gather*}
whose solution is described in Theorem 1 of the paper.
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