Lipschitz连续函数的α-Bernstein算子  

THEα-BERNSTEIN OPERATOR OF A LIPSCHITZ CONTINUOUS FUNCTION

作　　者：刘植[1] 王楚涵 陈晓彦[1] 檀结庆[1] LIU Zhi;WANG Chu-han;CHEN Xiao-yan;TAN Jie-qing(School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《数学杂志》2020年第4期408-414,共7页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China (11601115)

摘　　要：本文讨论了α-Bernstein算子与其逼近函数间的一个关系:若α-Bernstein算子满足Lipschitz连续,那么其逼近的函数也满足Lipschitz连续,反之亦然,而且α-Bernstein算子保持原来函数的Lipschitz常数.The relationship between theα-Bernstein operator and its approximation function is discussed in this paper.If theα-Bernstein operator belongs to the class of Lipschitz functions,then its approximation function f(x)also does,and vice versa.Moreover,theα-Bernstein operator can maintain the Lipschitz constant of the original function.

关 键 词：函数逼近 α-Bernstein算子 LIPSCHITZ连续 LIPSCHITZ函数 

分 类 号：O241.5[理学—计算数学]