On the fixed points of commuting nonexpansive maps in hyperconvex spaces

M. Amine Khamsi; Michael Lin; Robert Sine

doi:10.1016/0022-247X(92)90165-A

On the fixed points of commuting nonexpansive maps in hyperconvex spaces

M. Amine Khamsi, Michael Lin, Robert Sine

Mathematics

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21 Scopus citations

Abstract

Let {T₁, ..., T_N} be a finite commuting family of nonexpansive maps of a hyperconvex space such that each T_i has bounded orbits. We show: (i) Each point has a bounded orbit under the semigroup generated by {T_i}; (ii) There is a common fixed point for the family if (and only if) T = T₁T₂··· T_N 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 language	British English
Pages (from-to)	372-380
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	168
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(92)90165-A
State	Published - Aug 1992

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title = "On the fixed points of commuting nonexpansive maps in hyperconvex spaces",

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.",

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AU - Khamsi, M. Amine

AU - Lin, Michael

AU - Sine, Robert

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N2 - 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.

AB - 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.

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JF - Journal of Mathematical Analysis and Applications

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ER -

On the fixed points of commuting nonexpansive maps in hyperconvex spaces

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