Geodesic
Best methods of approximation and interpolation of differentiable functions in the space $C_{[-1,1]}$
Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 275-289 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. Bibliography: 6 titles. 
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     title = {Best methods of approximation and interpolation of differentiable functions in~the space $C_{[-1,1]}$},
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V. M. Tikhomirov. Best methods of approximation and interpolation of differentiable functions in the space $C_{[-1,1]}$. Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 275-289. http://geodesic.mathdoc.fr/item/SM_1969_9_2_a10/

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[2] V. M. Tikhomirov, “Odno zamechanie ob $n$-mernykh poperechnikakh mnozhestv v banakhovykh prostranstvakh”, Uspekhi matem. nauk, XX:1(121) (1965), 227–230

[3] V. M. Tikhomirov, “Nekotorye voprosy teorii priblizhenii”, DAN SSSR, 160:4 (1960), 774–777

[4] A. D. Ioffe, V. M. Tikhomirov, “Dvoistvennost vypuklykh funktsii i ekstremalnye zadachi”, Uspekhi matem. nauk, XXIII:6(144) (1968), 51–116 | MR | Zbl

[5] J. Singer, Cea mai buna aproximare in spatii vectoriale, Romania, 1967

[6] M. G. Krein, M. A. Krasnoselskii, D. P. Milman, “O defektnykh chislakh lineinykh operatorov v banakhovom prostranstve i o nekotorykh geometricheskikh voprosakh”, Sb. trudov in-ta matem. AN USSR, 11, 1948, 97–112