Multivariate Stancu operators defined on a simplex

摘要

In this paper, we introduce a sequence of multivariate linear operators called Stancu operators defined on a simplex, which generalizes the famous Bernstein operators. We first prove that when the parameter s in the definition of the Stancu operators is 0 or 1 the Stancu operators reduce to the Bernstein operators. Then, we give a symmetric property for these operators. Finally, we prove that the Lipschitz property of function is retained by the Stancu operators.