Fixed points in a group of isometries

Abstract

The Bruhat-Tits xed point theorem states that a group of isometries on a complete metric space with negative curvature possesses a xed point if it has a bounded orbit. This theorem is extended by a relaxation of the negative curvature condition in terms of the w-distance functions introduced by Kada et al. [Non-convex minimization theorems and xed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381-391].