抽象凸锥度量空间上集值映射的逼近连续选择及应用

Approximate Continuity Selection for Set-valued Maps in Abstract Convex Cone Metric Spaces and Application

利用抽象凸空间满足的H0条件和紧集的有限覆盖及与之相应的单位分解构造标准单纯形上的连续映射,从而由Brouwer不动点定理证明了抽象凸锥度量空间上具有邻域抽象凸值的锥度量上半连续集值映射的一个锥度量逼近连续选择定理,并由此得到具有邻域抽象凸值的锥度量上半连续集值映射的一个不动点定理,然后将此不动点定理应用于博弈论,通过构造锥度量上半连续最优反应集值映射得到抽象凸锥度量策略空间上的n人非合作广义博弈Nash平衡的一个存在性结果.

Constructing a continuity map on standard simplex by using H 0 condition of abstract convex space and the partition of unity subordinate to the finite covering of a compact set,a cone metric approximate continuity selection for cone metric upper semi-continuous set-valued maps in abstract convex cone metric spaces is proved by employing Brouwer fixed point theorem.Then a fixed point theorem for cone metric upper semi-continuous maps is derived.As an application,constructing cone metric upper semi-continuous best reflect map,the existence of Nash equilibrium of n-person non-cooperative generalized game with abstract convex cone metric strategy space is proved.