Uniform Approximation by the Class of Functions with Bounded Derivative

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.