关于q-Bernstein多项式及其Boole和迭代

Onq-Bernstein Polynomial and it's Iterated Boolean Sum

本文对q-Bernstein多项式Bn(f,q,x)收敛于B∞(f,q,x)的加速问题进行研究,同时对其Boolean和迭代的收敛性问题进行考虑.采用精细估计,并应用光滑模理论等手段,得到相应的逼近速度估计.结果表明:q-Bernstein多项式在这两个问题上与传统Bernstein多项式有着类似的结果.

In this paper,we investigate not only the acceleration proble about the q-Bernstein polynomial but also the convergence of it＇s iterated Boolean sum. Using the methods of exact estimate and theories of moduli of smoothness,we get the approximation rates which suggest that q- Bernstein polynomial has the similar answer with the classical Bernstein polynomial to these two problems,and reach a result similar with the classical Bernstein polynomial.