数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 142-153.

• 论文 • 上一篇    下一篇

Bernstein型算子同时逼近误差

丁春梅   

  1. 中国计量学院 理学院 杭州 310018
  • 收稿日期:2008-06-07 修回日期:2009-08-06 出版日期:2010-01-01 发布日期:2010-01-01
  • 基金资助:

    国家自然科学基金(90818020)和浙江省自然科学基金(Y7080235)资助.

The Errors of Simultaneous Approximation by Bernstein Type |Operators

DING Chun-Mei   

  1. College of Science, China Jiliang University, Hangzhou 310018
  • Received:2008-06-07 Revised:2009-08-06 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(90818020)和浙江省自然科学基金(Y7080235)资助.

摘要:

该文证明了C[0,1]空间中的函数及其导数可以用Bernstein算子的线性组合同时逼近, 得到逼近的正定理与逆定理. 同时, 也证明了Bernstein算子导数与函数光滑性之间的一个等价关系. 该文所获结果沟通了Bernstein算子同时逼近的整体结果与经典的点态结果之间的关系.

关键词: Bernstein 算子, 同时逼近, 正定理, 逆定理, 导数

Abstract:

In this paper,  we show that the functions in space C[0,1] and their derivatives can be simultaneously approximated by the combinations of the Bernstein operators. Both direct and inverse theorems are proved.   An equivalence relation between the derivatives of  the Bernstein operators and the smoothness of function is obtained as well.  These results bridge the gap between the classical  pointwise conclusions and the  global conclusions for simultaneous approximation by the Bernstein operators.

Key words: Bernstein operators, Simultaneous approximation, Direct theorem, Inverse theorem, Derivatives

中图分类号: 

  • 41A28