几类Lipschitz函数序列的逼近问题探讨  

Study of the Approximation Problem for Some Lipschitz Function Sequences

作　　者：李治[1] 何先平[1] 赵天玉[1] 陈忠[1] 

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《长江大学学报（自科版）（上旬）》2014年第2期1-5,共5页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目(11201039;61273179);湖北省教育厅重点项目(D20101304);长江大学自然科学培育项目(2013cjp09)

摘　　要：使用构造函数序列的方法,探讨了一致连续函数、连续函数、不连续函数(包括左连续和下半连续、右连续和上半连续、单调非降及左连续和有界、单调不增及右连续和有界)等几类较弱条件下的函数被Lipschitz函数序列的逼近问题,以在一些较弱的条件下确保微分方程解的存在唯一性。The method of constructing function sequence is used,the problems that are investigated,such as some functions with weaker condition such as uniformly continuous function,continuous function and discontinuous function(including left continuous and lower semi-continuous,right continuous and upper semi-continuous,monotone nondecreasing,left continuous and bounded,monotone nonincreasing,right continuous and bounded)are approximated by Lipschitz function sequence.

关 键 词：Lipschitz函数序列 一致连续函数 连续函数 不连续函数 逼近 

分 类 号：O211.63[理学—概率论与数理统计]