正线性算子对无穷区间上有界变差函数的点态逼近度

Pointwise Approximation for Functions of Bounded Variation on Infinite Interval by Positive Linear Operators

用ＢＶ［０，∞）表示在［０，∞）的每一有限子区间上为有界变差函数的函数构成的空间。用表示ＢＶ［０，∞）上的正线性算子，其中ｄｔＫｎ（ｘ，ｔ）是非负测度且，则有定理如果Ｌｎ（｜ｔ－ｘ｜β，ｘ）≤Ｃ（ｘ）／ｎｖ，，这里β＞０，ｖ≥１，Ｃ（ｘ）是一个与ｘ有关的常数，对ｆ∈ＢＶ［０，∞）和ｘ∈（０，∞）有这里作为应用，给出算子的逼近估计．

A poinwise approximation is given or functions of bounded varition on infinite interval by general positive linear operators.As an application,a pointiwise approximation with a Bernstein-type operator as defined by Bleimann,Butzer,and Habn is studied.