摘要
文章主要讨论了向量值函数的方向导数、Gateaux导数和Frechet导数的定义,并对它们之间的相互关系做了简单的讨论.证明了函数如果Frechet可微则一定Gateaux可微,如果Gateaux可微则一定方向可微;通过反例说明反之是不成立的,但增加一定的条件可使反过来也是成立的.最后还讨论了几个简单的性质.
The paper mainly discusses the directional differential, Gateaux differential and Frechet differential of vector valued functions, as well as the relationships between them. Proved that if a function is Frechet differenti- al, then it is Gateaux differential, if a function is Gateaux differential, then it is directional differential. Through the examples , we can see that the conclusions of opposite are not established, but increasing some conditions can make the opposite is also established. Finally, we also discussed several simple properties.
出处
《吉林师范大学学报(自然科学版)》
2014年第1期57-59,65,共4页
Journal of Jilin Normal University:Natural Science Edition
基金
湖北省教育科学"十二五"规划项目(2013B308)