Geodesic
Uniform Approximation by the Class of Functions with Bounded Derivative
Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 696-712.

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In the paper, the problem of uniform approximation of a continuous function defined on an interval is considered. The approximating functions have absolutely continuous derivatives of order $n-1$ and derivatives of order n bounded in absolute value. An alternance criterion for a best approximation element in this class is given. This criterion generalizes the criterion for the best approximation element obtained by N. P. Korneichuk in the class of Lipschitz functions. 
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     title = {Uniform {Approximation} by the {Class} of {Functions} with {Bounded} {Derivative}},
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A. V. Mironenko. Uniform Approximation by the Class of Functions with Bounded Derivative. Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 696-712. http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a5/

[1] Korneichuk N. P., Ekstremalnye zadachi teorii priblizheniya, Nauka, M., 1976 | MR

[2] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. M., Metody splain funktsii, Nauka, M., 1980 | MR

[3] Larry L. Schumaker, Spline functions: basic theory, New York, 1981 | MR

[4] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR