第二类Beta算子对一类导数有界函数的逼近

Rate of Convergence of Beta Operators of Second Kind for a Class of Bounded Functions with Derivatives

研究了第二类Beta算子的逼近性质,通过直接计算得到第二类Beta算子Ln(|t-x|,x)的一阶绝对矩的最优估计,由此估计结果结合Bojanic-Cheng-Khan的方法以及分析技巧,导出第二类Beta算子对一类导数有界函数的渐近估计,得出该算子的一个渐近展开公式.

This paper studies the approximation properties of Beta operators of second kind. The optimal estimate on the first order absolute moment of Beta type operators L.of second kind Ln（｜t-x｜,x） is obtained by direct computations. And then this estimate and Bojanic-Cheng-Khan;s method combining with analytical techniques are used to derive an asymptotically optimal estimation on the rate of convergence of Beta type operators L.of second kind for a class of bounded functions with derivatives.