Modulus of continuity, K-functional and Stancu operator on a simplex

In this paper, we introduce and study Stancu operator defined on a simplex, which generalizes the famous Bernstein operator. We first prove that the operator has a symmetric property for a transformation from the simplex to itself Then, we show that the operator can retain the property modulus of continuity. Finally, with a K-functional as metric, we establish direct, inverse and saturation theorems for the operator approximating the continuous. functions. The obtained results include some known conclusions, of the Bernstein operator.