有界线性空间中含有Q-距离的Ekeland变分原理  

A Ekeland's Variational Principle with Q-Distances on Bornological Vector Spaces

作　　者：武洁[1] 贺飞[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《应用泛函分析学报》2014年第2期183-188,共6页Acta Analysis Functionalis Applicata

基　　金：内蒙古自治区高等学校科学研究项目(NJZZ13019);内蒙古大学高层次人才引进科研项目(30105-125150);内蒙古大学校级创新训练计划(2012134)

摘　　要：有界线性空间中引入了Q-距离的概念,建立了一类向量值Ekeland变分原理,其目标函数是从有界线性空间映到锥序的实线性空间,并且扰动项中含有Q-距离.由此可以得到有界线性空间中现有的一些Ekeland变分原理.同时建立了有界线性空间中的向量值Caristi不动点定理,也给出二者的等价性.Q-distances are introduced on bornological vector spaces. A vectorial Ekeland＇s variational principle is established, where the objective function is from bornological vector spaces into real vector spaces, and its perturbation contains Q-distances. Moreover, some known Ekeland＇s variational principles are deduced. Meanwhile, a vectorial Caristi＇s fixed pointed theorem is obtained and the equivalence between two theorems is shown.

关 键 词：有界线性空间 EKELAND变分原理 CARISTI不动点定理 Q-距离 

分 类 号：O177.3[理学—数学]