Generalized KKM Theorems In L-convex Spaces And Applications

In the paper, new classes of generalized LKKM and generalized S-LKKM mappings in a nonempty subset of a L-convex space are obtained. Some new generalized LKKM and generalized S-LKKM theorems are established under the noncompact setting of a L-convex space. As applications, Some minimax inequalities and saddle point the-orems,fixed point theorems and section theorems, maximal element theorems and the existence theorems of equilibrium for abstract economies are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.