Cauchy积分中值定理逆问题的注记  

A Note on Inverse Problem of Cauchy's Integral Mid-VaIue Theorem

作　　者：王良成[1] 马秀芬[1] 杨明硕[1] WANG Liang Cheng;MA Xiu fen;YANG Ming Shuo(Chongqing Normal University, Foreign Trade And Business College, Chongqing 401520, China)

机构地区：[1]重庆师范大学涉外商贸学院,重庆401520

出　　处：《大学数学》2017年第5期86-91,共6页College Mathematics

基　　金：重庆师范大学涉外商贸学院重点科研项目(KY2015001)

摘　　要：使用函数严格单调性,获得了定积分的若干性质.应用这些性质,解决了Cauchy积分中值定理中值点的唯一性,并得到了该定理及其逆定理的较弱表述,进一步解决了其逆定理中积分区间端点的唯一性.Using the strictly monotone function,some properties of definite integral are obtained.Appling these properties,we solve the uniqueness of the median point for Cauchy’s integral mid value theorem,and obtain the weaker expression of this theorem and its inverse theorem,and further solve the uniqueness of integral interval end point for this inverse theorem.

关 键 词：Cauchy积分中值定理 严格单调性 左右极限 连续 逆问题 

分 类 号：O178[理学—数学]