摘要
基于对弱伪连续实值函数的研究,提出向量值函数关于锥的弱伪连续定义,并建立了向量值函数R_＋~k弱伪连续与实值函数弱伪连续的对应关系.作为弱伪连续向量值函数的应用,给出了弱伪连续下的向量值Ky Fan点的存在性定理,并通过该定理证明了伪连续向量值支付下的多目标博弈弱Pareto-Nash平衡点的存在性定理.
In this paper,based on the study of pseudocontinuous real-valued functions,a definition of the weakly pseudocontinuous of vector-valued functions on cone is proposed.And a weakly pseudocontinuous relationship is established between the vectorvalued functions on R_＋~k and the real-valued functions.As an application of the weakly pseudocontinuous of vector-valued functions on cone,the existence theorem of weakly Pareto-Nash equilibrium in multi-objective games with the pseudocontinuous payoffs is proved by the improved vector-valued Ky Fan points.
出处
《运筹学学报》
CSCD
北大核心
2015年第1期92-98,共7页
Operations Research Transactions
基金
上海自然科学基金(No.09ZR1411100)
上海市重点学科基金(No.S30104)
关键词
弱伪连续
向量值函数
向量值函数Ky
Fan点
多目标博弈
weakly pseudocontinuous
vector-valued functions
vector-valued Ky Fan points
multi-objective games
