加权范数下Durrmeyer型算子组合的一个逆定理(英文)

An Inverse Theorem for Combinations of Durrmeyer-type Operators in Weighted Norm

本文研究了Szasz-Mirakjan-Durrmeyer算子线性组合的加权逼近,这里的权函数w(x)=x~α(1+x)~β,—1/p<α<1—1/p,β是任意的实数,1≤p≤∞,得到如下结果: 定理:设φ(x)=x^(1/2),wf∈L_p[0,∞),0<λ<r,则下列命题等价: (Ⅰ) (Ⅱ) (Ⅲ)

In this paper, we investigate the weighted approximation in L_p[0,∞), where the weighted function w(x)=x~α(1+α)~β, -1/p<α<l-1/p,β is arbitrary, 1≤p≤∞. Our main result is given as follows. Theorem Let φ(x)=(1/2)x,wf∈L_p [0,∞) ,0<λ<r, then, the following statements are equivalent: