Uniform approximation by the class of functions with bounded derivative

作     者：Mironenko, AV 

作者机构：Russian Acad Sci Ural Div Math & Mech Inst Moscow 117901 Russia 

出 版 物：《MATHEMATICAL NOTES》 (数学札记)

年 卷 期：2003年第74卷第5-6期

页      面：656-670页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：approximation of functions splines alternance Budan-Fourier theorem 

摘      要：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.