Two porosity theorems for nonexpansive mappings in hyperbolic spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Reich, Simeon¹  Zaslavski, Alexander J.¹ 

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

关键词: Complete metric space;    Contractive mapping;    Fixed point;    Hyperbolic space;    Nonexpansive mapping;    Porous set;   

DOI  :  10.1016/j.jmaa.2015.08.043

来源: Elsevier

【 摘 要 】

In a previous paper of ours we used the notion of porosity to show that most of the nonexpansive self-mappings of bounded, closed and convex subsets of a Banach space are contractive and possess a unique fixed point which is the uniform limit of all iterates. In this paper we extend this result to nonexpansive self-mappings of closed and convex sets in a Banach space which are not necessarily bounded. As a matter of fact, it turns out that our results are true for all complete hyperbolic metric spaces. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free