摘要
本文讨论修正Durrmeyer-Bernstein算子D_n(f;x)的一个性质。即f(x)与D_n(f;x)属于同一Lipschitz类。
The modified Durrmeyer-Bernstein operator is defined as follow:■)_n(f; x)=sum from k=0 to n Φ_(n, k)(f)(■)x^k(1-x)^(n-k), x∈[0,1], f∈C[0,1], whereΦ_(n, 0)(f)=f(0); ωhen 1≤k≤n-1, Φ_n, _k(f)=(n-1)integral from n=0 to 1 f(t)P_(n-2), _(k-1)(t)dt here P_(nk)(t)-(■)t^k(1-t)^(n-k); Φ_n, _n(f)=f(1). The Lipschitz property of (■)_n(f; x) for f∈Lipμ ωas considered. Prove that (■)_n(f;x) and f are in the same Lipschitz class.
出处
《宁夏大学学报（自然科学版）》
CAS
1990年第1期18-22,共5页
Journal of Ningxia University(Natural Science Edition)
关键词
B-多项式
D-B算子
李普希兹类
Berntein polynomials, Wodified Durrmeyer-Berntsein operator, Lipschitz class.
