向量值函数的导数

Differential of Vector Valued Functions

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.