一类λ型的Bernstein算子列的逼近性质

On the Rate of Convergence of a New Family of λ Type Bernstein Operators

根据经典的Bojanic-Cheng分解方法,结合分析技术,研究了一类新型的Bernstein算子列对一类导数为有界变差的函数类的逼近.首先由蔡清波关于一阶二阶矩的结论得到一阶中心绝对矩■的估计,接着估计了另外一项■,最后得到该新型算子的收敛阶估计.

By using Bojanic-Cheng’s method and analysis techniques,the authors studied the rate of convergence of a new family of Bernstein operators for some absolutely continuous functions with a derivative equivalent to a bounded variation.By the result of Cai qingbo about the operator’s first moment and second moment,the authors obtained the first central absolute moment Bn,λ(|t-x|,x).Later,the other part Bn,λ(∫x^tφx(u)du,x) was estimated.Finally,the convergence rate of the new type operators was obtained.