完备随机度量空间上Ekeland变分原理与Caristi不动点定理的等价性  

Equivalence of Ekeland Variational Principle and Caristi Fixed Point Theorem in Complete Random Metric Spaces

作　　者：杨玉洁[1] 李翀[1] 

机构地区：[1]北京联合大学基础课教学部,北京

出　　处：《应用数学进展》2019年第10期1632-1635,共4页Advances in Applied Mathematics

基　　金：国家自然科学基金(No: 11601030);北京市自然科学基金(No: 1194022);“十三五”时期北京市属高校高水平教师队伍建设支持计划(No: CIT&TCD201704071);北京联合大学人才强校优选-百杰计划(项目号:BPHR2018CZ09)。

摘　　要：首先证明了在(ε,λ)-拓扑下完备随机度量空间上的Ekeland变分原理与Caristi不动点定理是等价的。再者,利用两种拓扑下基本结果之间的关系,证明了在特殊的随机度量空间——随机赋范模上,两者在两种拓扑下都是等价的;最后由完备随机赋范模上的Caristi不动点定理,在两种拓扑下建立了完备随机赋范模上的方向压缩不动点定理。Firstly, it is proved that Ekeland variational principle is equivalent to Caristi fixed point theorem on complete random metric spaces under(ε,λ)-topology. Furthermore, making use of the relationship of the basic results between the two topologies, we prove that in the special random metric space—the random normed model, they are equivalent in both topologies. Finally, from Caristi fixed point theorem on complete random normed modules, the directional fixed point theorems are established on complete random normed modules under two topologies.

关 键 词：随机度量空间 随机赋范模 EKELAND变分原理 CARISTI不动点定理 

分 类 号：G63[文化科学—教育学]