Intersection theorems and their applications in general almost convex spaces

In this paper, we extend the concept of the almost convex condition and establish an approximation property for convex continuous correspondences. We use the approximation property to generalize von Neumann’s intersection theorems and related topics. We obtain, as applications, some new equilibrium theorems for the existence of a maximal element, generalized games, and qualitative games of UU-majorized correspondences.