Convergence Properties and Characterization of Convergence Order for Multivariate q-Stancu Polynomials
多元q-Stancu多项式的收敛性及其收敛阶刻画

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.