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.
出处
《系统科学与数学》
CSCD
北大核心
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
