单纯形上的q-Stancu多项式的最优逼近阶  

Optimal Approximation Order for q-Stancu Operators Defined on a Simplex

作　　者：李风军[1] 徐宗本[1] 郑开杰[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《数学学报（中文版）》2008年第1期135-144,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(60575045)

摘　　要：构造了单纯形上的多元q-Stancu多项式,它是著名的Bernstein多项式和Stancu多项式的推广.建立该类多项式逼近连续函数的上、下界估计,进而给出其对连续函数的最优逼近阶(饱和阶)及其特征刻画.此外,还研究了该类多项式逼近连续函数的饱和类.In this paper, a kind of multivariate linear operators, q-Stancu operators, are defined on a simplex, which generalize the famous Bernstein operators and Stancu operators. By establishing the upper and lower bound estimations of approximation order, the optimal approximation order （saturation order） and the characteristics of these operators approximating the continuous functions are characterized. Moreover, the saturation class of approximation is confirmed.

关 键 词：q-Stancu多项式 逼近阶 单纯形 

分 类 号：O174.41[理学—数学]