Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
N. P. Korneichuk, Extremal Problems of the Approximation Theory [in Russian], Nauka, Moscow, 1976.
Yu. S. Zav'yalov, B. I. Kvasov, and V. M. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow, 1980.
Larry L. Schumaker, Spline Functions: Basic Theory, New York, 1981.
N. P. Korneichuk, Exact Constants in the Approximation theory [in Russian], Nauka, Moscow, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mironenko, A.V. Uniform Approximation by the Class of Functions with Bounded Derivative. Mathematical Notes 74, 656–670 (2003). https://doi.org/10.1023/B:MATN.0000008998.41243.75
Issue Date:
DOI: https://doi.org/10.1023/B:MATN.0000008998.41243.75