Nonempty intersection theorems in topological spaces with applications

In this paper,we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces.As applications,an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces.Our results generalize some known results in the literature.