Generalized -KKM type theorems in topological spaces with an application

In this paper, we first introduce a new concept of generalized L-KKM mapping and establish some new generalized L-KKM type theorems without any convexity structure in topological spaces. As an application, an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem is proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.