(1) Department of Mathematics, Shaoxing College of Arts and Sciences, 312000 Shaoxing Zhejiang Province, P. R. China;(2) Xi'an Jiaotong University, 710049 Xi'an, P. R. China
Abstract:
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. Supported by Foundation of Key Item of Science and Technology of Education Ministry of China (03142), Foundation of Higher School of Ningxia (JY2002107) and Nature Science Foundation of Zhejiang Province(102002).
