Multivalued fixed point theorems without strong compactness via a generalization of midpoint convexity
The paper introduces the notions of a strongly and weakly midpoint linear multivalued maps, convex and midpoint convex multivalued maps, studies relations between these concepts, sufficient and necessary conditions. Several results concerning the existence of fixed points of such maps are established. As it appears, the structural assumptions (involving the midpoint properties) along with upper-semicontinuity allow to relax the usual compactness conditions. The abstract results are applied to show the existence of equilibria for some specific \(n\)-player games.
scientific article; zbMATH DE number 6361893