Bernstein算子的点态同时逼近

Pointwise simultaneous approximation of Bernstein operator

借助光滑模W2Ф（f，t）（Ф是一般步权函数），研究了Bernstein算子的点态同时逼近问题，给出了Bernstein算子同时逼近的等价定理，建立了其导数与光滑函数间的关系，对以前已有的结果予以补充和完善．

In this paper, the simultaneous approximation of Bernstein operator is discussed using the modulus of smoothness w2Ф（f, t） （where Ф is the usual step weight function）, and several equivalent theorems of the simultaneous approximation are obtained. Moreover, the relation between the derivation of the Bernstein polynomial and the smoothness of the approximated function is revealed. These results complement and improve some known results.