Two porosity theorems for nonexpansive mappings in hyperbolic spaces

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• 作者：Simeon Reich ; ^{sreich@tx.technion.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Alexander J. Zaslavski ^{ajzasl@tx.technion.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Complete metric space ; Contractive mapping ; Fixed point ; Hyperbolic space ; Nonexpansive mapping ; Porous set
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1220-1229
• 全文大小：279 K

文摘

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.