扰动Fej\'{e}r点上复Hermite插值的联合逼近

$D$是复平面中由闭Jordan曲线$\Ga$围成的单连区域. 考虑在$\Ga$上扰动Fej\''er点的 Hermite插值一致逼近、平均逼近和联合逼近于函数$f\in A^{(q)}(\o D)$. 该文中的逼近阶一般说来是不可再改进的, 区域的边界限制条件到目前为止是最少的. 以往的全部同类结果都包括在该文中作为特殊情形, 由于该文方法上的改进, 简化和省去了以往 某些证明过程.

Simultaneous approximation by complex Hermite interpolation at disturbed Fejér points

Let D be a simply-connected domain bounded by a closed Jordan curve Г in the complex plane. We consider the uniform approximation, approximation in mean and simultaneous approximation to f∈A（q）（^-D） by Hermite interpolation at disturbed Fejér points on Г. In this paper, the orders of approximation, in general, can not be improved again and the assumption of the boundary condition is better than that in other work of the same class. Lots of similar results are included as particular cases, the method has been improved and some proofs are omitted in the present paper.