证明函数一致连续的几种方法

Some methods for proving function's consistent continuity

主要从五个方面探究证明函数一致连续的方法:从导函数判断函数是否一致连续;利用Lipschitz条件,推导出判断复合函数是否一致连续的方法;由函数定义域上数列的limn→∞xn存在,而nl→im∞(fxn)不存在,从而得(fx)不一致连续;从函数(fx)导数的极限判断函数一致连续;用另一个函数给出函数一致连续的充要条件。主要的研究方法是放缩条件、类比、等价转化。

This article discusses the methods for proving function＇s consistent continuity through five areas.first,using knowledge of derivative function searches for the ways of proving function＇s consistent continuity;second,using Lipschitz condition to judge whether the composite functions are consistent-continuity functions;third,limn→∞xnexists on the domain of a function,butlimn→∞（fxn）dose not exist,so （fx）is inconsistent-continuity function;fourth,using derivative function＇s limit to judge whether functions are consistent-continuity functions;fifth,using another function to give a necessary and sufficient condition of the function＇s consistent continuity.The main research methods of this paper are analogy,scaling condition and equivalent transformation.