伯恩斯坦多项式与其所逼近的连续函数

Bernstein polynomials and its approximating continuous functions

证明了如果线性正算子伯恩斯坦多项式属于李卜希兹函数类 Lip Mα,那末 ,它所逼近的函数 f (x)也属于李卜希兹函数类 L ip Mα.

Let Bernstein polynomials B n(f;x) be functions of order α,0<α≤1, on [0,1],its approximating continuous functions f(x) belongs to the same class of function Lip Mα.