用Feller算子逼近第一类间断点的函数

ON APPROXIMATION BY FELLER OPERATORS FOR FUNCTIONS HAVING DISCONTINUITY POINTS OF THE FIRST KIND

§1.引言 熟知,若f(x)定义在[0,1],著名的Bernstein算子由下式给出Herzog证明了,若x是f(x)的第一类间断点,则有 因而,若f(x)是[0,1]上有界变差函数,(1.2)应成立。文献[2]给出了相应的收敛速度。[3],[4]改进了[2]的结果。关于一些著名算子对有界变差函数的逼近,近来有不少研究,如[5—8]。最近,王美琴应用点态连续模,对[0,1]上只有第一类间断点的有界函数。

In this paper,we investigate the degree of approximation by Feller operators for funcations which have only discontinuity points of the first kind on [0,∞)with exponential growth.Our estimates are essentially the bestpossible.The results here include the results or partial resuits of the references[2,3,6,7,9]