Generalized L-KKM type theorems in L-convex spaces with applications

In this paper, a new notion of generalized L-KKM mappings is introduced. Some generalized L-KKM type theorems for generalized L-KKM mappings with finitely closed (or compactly closed) values and with finitely open (or compactly open) values are established in L-convex spaces. As applications, some Ky Fan type matching theorems, fixed-point theorems and minimax inequality are obtained in L-convex spaces. These results generalize a number of known results in recent literature.