Abstract: The new classes of L_Fc-correspondences and L_Fc -majorised correspondences without open lower sections is introduced. Some existence theorems of madximal elements of the L_Fc -correspondences and the L_Fc-majorized correspondences defined on noncompact set in topological vector spaces are obtained. As applications, some existence theorems of equilibrium points for one-person games, qualitative games and generalized games with the L_Fc -majorized correspondences devined on noncompact strategy sets in topological vector spaces are also given. These theorems improve and generalize several known results in recent literature.

Key words: Generalized games, L_Fc-majorized correspondence, transfer compactly openvalued, equilibrium