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

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.