关于Baskakov－Durrmeyer算子线性组合的加权逼近

Weighted Approximation by the Linear Conbination of Baskakov-Durrmeyer Operators in L_p

本文主要讨论了一类Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ算子线性组合的加权逼近问题，其中权函数为ω（ｘ）＝ｘａ（１＋ｘ）β；借助于Ｋ－泛函与Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ模的等价性，我们给出了加权逼近的特征刻划。

Abstract Let Mn(f;x)are the Baskakov-Durrmeyer operators:whereLn,f(f,x)are the linear cornbination of Mnj(f,x):In this paper,we consider the weighted approximation by Ln,f(f,x)in Lp[0,∞)with Jacobi weighted functionω(x)=xα(l+x)β,1≤P≤∞,βare arbitrary and our main results are following:Theorem 1.1 Let ω(X)f(x)∈LP[0,∞),l≤p≤∞,0<λ<r,then following statmentsare equivalent:where