Equilibria of nonparacompact generalized games with ℒcℒc-majorized correspondences in FC-spaces

The new concept of FC-hull for a nonempty subset in FC  -spaces is introduced, which includes the convex hull in topological vector spaces, the HH-convex hull in HH-spaces and GG-convex hull in GG-convex spaces as special cases. On this basis, new classes of ℒcℒc-correspondences and ℒcℒc-majorized correspondences without open lower sections are introduced in FC  -spaces. Some existence theorems of maximal elements for ℒcℒc-correspondences and ℒcℒc-majorized correspondences are proved in FC  -spaces. As applications, some equilibrium existence theorems for qualitative games and generalized games with infinite set of players and ℒcℒc-majorized correspondences are established in FC-spaces. These results unify, improve and generalize many corresponding results in recent literature.