修正的Szász-Mirakjan算子的逼近性质

Some properties of approximation of the modified Szasz-Mirakjan operators

研究了修正的Szasz—Mirakjan算子对一类绝对连续函数的逼近．首先计算该算子的一阶中心绝对矩，然后估计了另外一项S^＊n（∫^trφ（u）du,x）,最后利用Bojanic—Cheng方法，结合分析技术得到比较精确的收敛阶及渐近展开式．

We investigate the rate of convergence of the operators for some absolutely continuous functions. Inthe first, we compute the first central absolute moment, then the other part S^＊n（∫^trφ（u）du,x）is estimated.Lastly, an asymptotically optimal estimate is obtained by Bojanic-Cheng＇s method and analysis techniques.