Abstract
Abstract 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.
Highlights
1 Introduction Fixed point theorems for set-valued mappings play a vital role in various fields of pure and applied mathematics
The Browder fixed point theorem is called in the literature the Fan-Browder fixed point theorem
A body of generalizations and applications of the Fan-Browder fixed point theorem have been extensively investigated by many authors; see, for example, [ – ] and the references therein
Summary
Fixed point theorems for set-valued mappings play a vital role in various fields of pure and applied mathematics.
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