q-Stancu算子的保形性及收敛定理  

Shape-preserving and convergence properties of q-Stancu operator.

作　　者：云连英[1] 

机构地区：[1]浙江台州职业技术学院,浙江台州318000

出　　处：《浙江大学学报（理学版）》2009年第3期254-258,共5页Journal of Zhejiang University（Science Edition）

基　　金：浙江省教育厅科研项目(20071078)

摘　　要：给出了基于q-整数的Stancu算子Ln(.,q),同时研究了该算子的一些基本性质.首先,利用q-Stancu算子作用于某一函数f(x)以后Ln(f,q;x)与f(x)变号数的关系,得到了该算子的保形性定理.其次,通过精细的不等式放缩,该算子作用于一般的连续函数后收敛于一极限算子,而不像一般算子那样收敛于函数本身,并用光滑模刻画了其收敛速度.A generalization of Stancu operator based on q-integer is introduced. And some essential properties of this operator are investigated. One of these properties is the shape-preserving property which is studied with the help of the sign changes of f（x） and Ln （f,q;x）. The other is the convergence property. On this aspect, q-Stancu operator behaves quite differently compared with the usual operator such as Bernstein operator, Stancu operator and so on.

关 键 词：STANCU算子 q-整数 保形性 变号数 收敛速度 

分 类 号：O174.41[理学—数学]