Bernstein型算子同时逼近误差  

The Errors of Simultaneous Approximation by Bernstein Type Operators

作　　者：丁春梅[1] 

机构地区：[1]中国计量学院理学院,杭州310018

出　　处：《数学物理学报（A辑）》2010年第1期142-153,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(90818020);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.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.

关 键 词：BERNSTEIN算子 同时逼近 正定理 逆定理 导数. 

分 类 号：O174.41[理学—数学]