正方形上的Lipschitz连续函数的Bernstein多项式的Lipschitz常数

Lipschitz Constants for Bernstein Polynomials of a Lipschitz Continuous Function over the Square

定义在正方形上的Lipschitz连续函数的Bernstein多项式仍是Lipschitz函数,且Lipschitz常数不变。

We present the result of the Lipschitz constants for the Bernstein polynomials B_(n,m)(f) of a Lipschitz continuous function fover the square I=[0,1]×[0,1], i. e. If f∈Lip_Aμ, then for all n,m≥1, B_(n,m)(f)∈Lip_Aμ.