Collectively fixed point theorems in noncompact abstract convex spaces with applications

Abstract

In this paper, by using the KKM theory and the properties of Γ-convexity and RC-mapping, we investigate the existence of collectively fixed points for a family with a finite number of set-valued mappings on the product space of noncompact abstract convex spaces. Consequently, as applications, some existence theorems of generalized weighted Nash equilibria and generalized Pareto Nash equilibria for constrained multiobjective games, some nonempty intersection theorems with applications to the Fan analytic alternative formulation and the existence of Nash equilibria, and some existence theorems of solutions for generalized weak implicit inclusion problems in noncompact abstract convex spaces are given. The results obtained in this paper extend and generalize many corresponding results of the existing literature.

Keywords

• abstract convex space
• collectively fixed point
• nash equilibrium
• nonempty intersection theorem
• generalized weak implicit inclusion problem