Bernstein-Durrmeyer算子拟中插式在Orlicz空间中的逼近
APPROXIMATION BY BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN ORLICZ SPACES

本文在Orlicz空间中研究了Bernstein-Durrmeyer算子拟中插式Bn（2r-1）（f，x）逼近性质.利用2r阶Ditzian-Totik模与K-泛函的等价性，Jensen不等式，H？lder不等式，Berens-Lorentz引理得到了逼近的正，逆和等价定理，从而推广了Bernstein-Durrmeyer算子拟中插式Bn（2r-1）（f，x）在LP空间的逼近结果.
In the present paper, we will study the approximation property of the BernsteinDurrmeyer quasi-interpolants Bn(2r-1)(f,x) in Orlicz space. By using the 2r-th Ditzian-Totik modulus of smoothness, Jensen inequality, H？lder inequality and Berens-Lorentz lemma, we obtain the direct, inverse and equivalence theorems, which generalize the approximation results of the Bernstein-Durrmeyer quasi-interpolants Bn(2r-1)(f,x) in LP space