Approximation of Generalized Bernstein Operators  

作　　者：Xiru Yang Chungou Zhang Yingdian Ma 

机构地区：[1]School of Mathematical Sciences, Capital Normal University [2]Department of Information Administration, The Central Institute for Correctional Police

出　　处：《Analysis in Theory and Applications》2014年第2期205-213,共9页分析理论与应用（英文刊）

基　　金：Supported by the Natural Science Foundation of China (No. 11271263, 11371258)

摘　　要：This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 （f,t）=O（t^α）←→｜Cn（f,sn,x）-f（x）｜=O（（n^-1/2δn^1-λ（x））^α）,where δn^2（x）=max{φ^2（x）,1/n} and 0〈α〈2.This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 （f,t）=O（t^α）←→｜Cn（f,sn,x）-f（x）｜=O（（n^-1/2δn^1-λ（x））^α）,where δn^2（x）=max{φ^2（x）,1/n} and 0〈α〈2.

关 键 词：Bernstein type operator Ditzian-Totik modulus direct and converse approximation theorem. 

分 类 号：O177[理学—数学]