局部Lipschitz函数的方向导数及应用

局部Lipschitz函数的方向导数及应用

摘  要

本文的第1部分对局部Lipschitz函数的Clarke方向导数及强Clarke方向导数给出了的定义，讨论了Clarke方向导数及Clarke强方向导数的性质；第2部分给出局部Lipschitz函数广义方向导数的Ky Fan不等式；第3部分讨论Clarke方向导数的Ky Fan型不等式对不动点定理的应用．
关键词：Clarke方向导数;强Clarke方向导数；局部Lipschitz函数；Ky Fan不等式；正规锥；正切锥；不动点定理

Directed Derivative of Locally Lipschitz Functions and Its Application

ABSTRACT
The definition of strong Clarke’s directed derivative of local Lipschitz function is given in the first part of this paper and the properties of Clarke directed derivative and strong Clarke’s directed derivative are discussed too; Ky Fan’s type inequality of generalized directed derivative of local Lipschitz is given in the second part. Finally,we discussed the applications of Ky Fan’s type inequality of Clarke’s directed derivative to Fixed Point theorems.
Keywords: Clarke directed derivative; Locally Lipschitz Functions; Ky Fan inequality;Tangent cone; Normal cone;
Fixed point theorems.