L^p APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

摘要

As a generalization of the Bernstein-Durrmeyer operators defined on the simplex, a class of general Bernstein- Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decomposition way. From the theorems the characterization of Lp approximation behavior is derived.