多元q-Stancu多项式的收敛性及其收敛阶刻画  

CONVERGENCE PROPERTIES AND CHARACTERIZATION OF CONVERGENCE ORDER FOR MULTIVARIATE q-STANCU POLYNOMIALS

作　　者：李风军[1] 徐宗本[2] 李星[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021 [2]西安交通大学理学院信息与系统科学研究所,西安710049

出　　处：《系统科学与数学》2009年第1期70-79,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10371097);宁夏大学自然科学基金(ZR200803)资助课题

摘　　要：定义单纯形上的多元q-Stancu多项式,它是著名的Bernstein多项式,q-Bernstein多项式,Stancu多项式的推广.以多元函数的部分连续模及全连续模为度量,建立推广的多元q-Stancu多项式对连续函数的一致收敛定理与收敛阶估计,并以实例加以验证.As a generalization of the Bernstein polynomials, the q-Bernstein polynomials and the Stancu polynomials, a class of broader polynomials called the multivariate q-Stancu polynomials defined on the normal simplex is introduced. With the partial continuity modulus and the full continuity modulus of multivariate function as a metric, the uniform convergence theorem of the generalized multivariate Stancu polynomials to any continuous functions is proved, and the estimation of the convergence order is also obtained. Finally, an example shows the validity of the obtained result.

关 键 词：单纯形 q-Stancu多项式 一致收敛 连续模 

分 类 号：O174.14[理学—数学]