拓扑向量空间中的W-距离和向量值Ekeland变分原理(英文)  

W-distance on topological vector spaces and vectorial Ekeland's variational principle

作　　者：贺飞[1,2] 丘京辉[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《苏州大学学报（自然科学版）》2010年第2期30-34,共5页Journal of Soochow University(Natural Science Edition)

基　　金：the National Natural Science Foundation of China(10871141)

摘　　要：类似于度量空间中的W-距离,给出拓扑向量空间中的W-距离.由此,我们推出一个向量值Ekeland变分原理,其目标函数是从具有W-距离的拓扑向量空间到拓扑向量偏序空间.同时,获得了Caristi不动点定理和Takahashi非凸极小化定理而且证明了三个定理之间是等价的.Similar to the W-distance on metric spaces,a W-distance on topological vector spaces is given.From this,we deduce a vectorial Ekeland＇s varicational principle,where the objective function is from topological vector spaces with a W-distance into partial ordered topological vector spaces.Meanwhile,a vectorial Caristi＇s fixed point theorem and a vectorial Takahashi＇s nonconvex minimization theorem are obtained and the equivalencers between the three theorems are shown.

关 键 词：EKELAND变分原理 CARISTI不动点定理 Takahshi非凸极小化定理 拓扑向量空间 W-距离 

分 类 号：O177.3[理学—数学]