非连续导函数的局部保号性  

Local-infinite Sign-preserving Property of Derivable Functions

作　　者：杨松林[1] YANG Song-lin(School of Mathematical Sciences and Wenzheng College,Soochow University,Suzhou Jiangsu215006,China)

机构地区：[1]苏州大学数学科学学院和文正学院

出　　处：《大学数学》2019年第6期66-69,共4页College Mathematics

基　　金：国家自然科学基金资助项目(11171246);苏州大学教材培育项目—文科数学(5831501718)

摘　　要：局部保号性是连续函数的一个重要性质,在已有文献基础上进一步讨论函数的局部保号性,给出了导函数在非连续点处的一个局部无限保号性.设f(x)是区间I上的可导函数,f′(x0)>0(其中x0∈I,f′(x)在x0处不必连续),则任给x0的开邻域■是区间I的无限子集.这一结果进一步深化了函数在非连续点处的局部保号性理论.Local sign-preserving property is an important property of continuous functions.In this paper,based on the study on various literatures,further study on the local sign-preserving property has been done and a local infinite sign-preserving property of derivative function at discontinuous point has been obtained.Let f(x)be a derivable function on a interval I,x0∈I and f′(x0)>0,then for any open neighborhood Uof x0,■is an infinite subset of I.This result further deepens the local sign-preserving property theory of functions at discontinuous points.

关 键 词：连续函数 导函数 保号性 离散子集 

分 类 号：O172.1[理学—数学]