多元q-Stancu多项式的收敛性及其收敛阶刻画

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.

Convergence Properties and Characterization of Convergence Order for Multivariate q-Stancu Polynomials

As a generalization of the Bernstein polynomials, the q-Bernstein polynomialsand the Stancu polynomials, a class of broader polynomials called the multivariateq-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.