Approximation of Generalized Bernstein Operators

作     者：Xiru Yang Chungou Zhang Yingdian Ma 

作者机构：School of Mathematical Sciences Capital Normal University Department of Information Administration The Central Institute for Correctional Police 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2014年第30卷第2期

页      面：205-213页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：Bernstein type operator Ditzian-Totik modulus direct and converse approximation theorem. 

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 follows ωφλ^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.