关于SBK平移算子r阶导数的迭代极限

On the limit of iterates of rth derivative of translation SBK operator

本文给出了SBK平移算子任意阶导数的迭代极限和迭代误差估计式,并证明了当f^(r)(x)为[0,1]上的连续函数,n→∞时,该迭代极限为 (1-x)f^(r)(0)+xf^(r)(1).

In this paper, the limit of iterates and estimation of iterates error of rth derivative of translation SBK operator were given. The limit of iterates was is a continuous function within the closed interval [0,1] and as n approaches infinity as a limit