Abstract: 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.

Key words: generalized L-KKM mapping, L-diagonally quasi-subspace, transfer compactly closed-valued, fixed point, quasi-equilibrium problem