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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 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	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 - 1 Jan 1992

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

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

Cite this

@article{e5dd1dfd2d5144e39959eba977cdf9fa,

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.",

author = "Khamsi, \{M. Amine\} and Michael Lin and Robert Sine",

year = "1992",

month = jan,

day = "1",

doi = "10.1016/0022-247X(92)90165-A",

language = "English",

volume = "168",

pages = "372--380",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - On the fixed points of commuting nonexpansive maps in hyperconvex spaces

AU - Khamsi, M. Amine

AU - Lin, Michael

AU - Sine, Robert

PY - 1992/1/1

Y1 - 1992/1/1

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.

UR - https://www.scopus.com/pages/publications/38249010780

U2 - 10.1016/0022-247X(92)90165-A

DO - 10.1016/0022-247X(92)90165-A

M3 - Article

AN - SCOPUS:38249010780

SN - 0022-247X

VL - 168

SP - 372

EP - 380

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On the fixed points of commuting nonexpansive maps in hyperconvex spaces

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this