有界线性空间中的向量值Ekeland变分原理(英文)  

A Vectorial Ekeland's Variational Principle on Bornological Vector Spaces

作　　者：贺飞[1,2] 丘京辉[2] 

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

出　　处：《数学进展》2013年第6期889-895,共7页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.10871141);Scientific Studies of Higher Education Institution of Inner Mongolia(No.NJZZ13019)

摘　　要：本文建立了一个向量值Ekeland变分原理,其目标函数是从有界线性空间到实线性空间,而且实线性空间中的序锥不需要是实体的.同时,获得了向量值Caristi不动点定理和向量值Takahashi非凸极小化定理,而且证明了三个定理是等价的.We establish a vectorial Ekeland＇s variational principle where the objective function is from bornological vector spaces into real vecto, spaces, and the ordering cone in real vector spaces is not necessarily solid. Meanwhile, a vectorial Caristi＇s fixed point theorem and a vectorial Takahashi＇s nonconvex minimization theorem are obtained and the equivalences between the three theorems are shown.

关 键 词：EKELAND变分原理 CARISTI不动点定理 Takahashi非凸极小化定理 有界线性空间 实线性空间 

分 类 号：O177.3[理学—数学]