Minimax inequalities for functions with noncompact domain and diagonal GC-quasiconcavity and their applications

Abstract

This paper introduces the notion of diagonal GC-quasiconcavity which generalizes the notions of quasiconcavity, CF-quasiconcavity, diagonal transfer quasiconcavity, C-quasiconcavity, diagonal C-concavity, and diagonal C-quasiconcavity. We first establish some theorems for the existence of ?-equilibrium of minimax inequalities for functions with noncompact domain and diagonal GC-quasiconcavity in topological spaces without linear structure. Next, we apply these results to characterize the existence of saddle points and solutions to the complementarity problem. Finally, we derive some intersection theorems and their equivalent forms.