修正的Bernstein算子的点态逼近性质

The pointwise approximation properties for the modified Bernstein operators

为改善算子的逼近速度,许多学者对一些著名的线性算子进行修正。King J P把Bernstein算子修正为算子Ln(f,x),并利用古典光滑模ω(f,t)研究了算子Ln(f,x)的收敛速度。利用统一光滑模ωφλ(f,t)来刻划Ln(f,x)的逼近性质,首先利用光滑K-泛函的等价性得到点态逼近正定理,其次对算子导数进行了估计,进而证明了等价定理.所得结果扩展了以前的一些结果。

In order to improve the approximation rate of the operators, many scholars have modified some famous linear operators. King J P has modified Bernstein operators into the operators Ln （f,x） and researched the convergent rate of L,（f,x） by the classic module ω（f,t）. By mean of the unified module of smoothness ωφλ （f,t）, the approximation properties of Ln（f,x） are shown. Firstly, using the equivalent relations between module of smoothess and K -functional, the poinwise direce theorem is obtained. Secondly, the estimate of derivatives of operators is obtained and the equivalent theorem is proved. The results expand the previous ones.