含有Dini导数的微分中值定理的逆定理  

THE INVERSE THEOREMS OF DIFFERENTIAL MEAN VALUE THEOREMS WITH DINI DERIVATIVE

作　　者：布仁白乙拉[1] 苏雅拉图[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古农业大学学报（自然科学版）》2016年第5期134-140,共7页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：内蒙古自治区自然科学基金项目(2012MS1022);内蒙古师范大学人才工程基金项目(RCPY-2-2012-K-034)

摘　　要：Dini导数是分析学中一般导数的推广形式,它在稳定性理论、模糊数学和优化问题中均有应用.本文给出了含有Dini导数的Lagrange中值定理和Cauchy中值定理在某种条件下的逆定理,并给出了其证明.Dini derivative is the generalized form of the general derivative in mathematical analysis, and it is applied in the stability theory, fuzzy mathematics and optimization problems. In this paper, the inverse theorems of Lagrange mean value theorem and Cauchy mean value theorem with the Dini derivative are established under certain conditions. The proofs of these inverse theorems are given.

关 键 词：DINI导数 微分 中值定理 逆问题 

分 类 号：O171[理学—数学]