On the fixed points of commuting nonexpansive maps in hyperconvex spaces

M. Amine Khamsi, Michael Lin, Robert Sine

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Let {T1, ..., TN} be a finite commuting family of nonexpansive maps of a hyperconvex space such that each Ti has bounded orbits. We show: (i) Each point has a bounded orbit under the semigroup generated by {Ti}; (ii) There is a common fixed point for the family if (and only if) T = T1T2··· TN has a fixed point; (iii) For each ε > 0, there is a nonempty set of common ε-approximate fixed points for the family. Some additional related results are also given.

Original languageEnglish
Pages (from-to)372-380
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume168
Issue number2
DOIs
StatePublished - 1 Jan 1992

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