Orlicz空间内正系数代数多项式倒数对非负连续函数的逼近

ON APPROXIMATION OF NON-NEGATIVE CONTINUOUS FUNCTION BY RECIPROCALS OF POLYNOMIAL WITH POSITIVE COEFFICIENTS IN ORLICZ SPACES

本文研究了Bernstein-Durrmeyer代数多项式倒数对非负连续函数在Orlicz空间中的逼近问题.利用光滑模和K-泛函等工具,获得了收敛速度的估计,所得的结果比Lp空间内的相应结果具有拓展的意义.

In this paper, we study the approximation problem of non-negative continuous functions by reciprocals of Bernstein-Durrmeyer polynomial in Orlicz spaces by using K-functional and modulus of smoothness, and the results are more significant than the corresponding results of Lp space.