In this paper, we found a new result by relaxing the condition of [15, Corollary 2]. As its application, we have obtained some new minimax inequalities of Ky Fan and minimax theorems in the spaces without linear structure.
In this paper, noncompact CAT(0) versions of the Fan-Browder fixed point theorem are established. As applications, we obtain new minimax inequalities, a saddle point theorem, a fixed point theorem for single-valued mappings, best approximation theorems, and existence theorems of ϕ-equilibrium points for multiobjective noncooperative games in the setting of noncompact CAT(0) spaces. These results generalize many well-known theorems in the literature. MSC: 91A10; 47H04; 47H10; 54H25
A new intersection theorem is obtained in L-convex spaces without linear structure. As its applications, a fixed point theorem, a maximal element theorem, a coincidence theorem, some new minimax inequalities and a saddle point theorem are given in L-convex spaces. Our results generalize many known theorems in the literature. 2005 Published by Elsevier Inc.
The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.
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