Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

C. E. Chidume, Habtu Zegeye, Naseer Shahzad

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

Original languageEnglish
Pages (from-to)233-241
Number of pages9
JournalFixed Point Theory and Applications
Volume2005
Issue number2
DOIs
Publication statusPublished - Dec 1 2005

Fingerprint

Nonexpansive Mapping
Common Fixed Point
Convergence Theorem
Closed
Fixed Point Property
Subset
Retract
Retraction
Banach spaces
Strong Theorems
Set theory
Strong Convergence
Differentiable
Banach space
Norm
Family

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Applied Mathematics

Cite this

@article{1bfc09dbdf814c94b5e5fdbd57319564,
title = "Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings",
abstract = "Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly G{\^a}teaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.",
author = "Chidume, {C. E.} and Habtu Zegeye and Naseer Shahzad",
year = "2005",
month = "12",
day = "1",
doi = "10.1155/FPTA.2005.233",
language = "English",
volume = "2005",
pages = "233--241",
journal = "Fixed Point Theory and Applications",
issn = "1687-1820",
publisher = "Springer Publishing Company",
number = "2",

}

Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings. / Chidume, C. E.; Zegeye, Habtu; Shahzad, Naseer.

In: Fixed Point Theory and Applications, Vol. 2005, No. 2, 01.12.2005, p. 233-241.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

AU - Chidume, C. E.

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2005/12/1

Y1 - 2005/12/1

N2 - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

AB - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

UR - http://www.scopus.com/inward/record.url?scp=33749552101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749552101&partnerID=8YFLogxK

U2 - 10.1155/FPTA.2005.233

DO - 10.1155/FPTA.2005.233

M3 - Article

AN - SCOPUS:33749552101

VL - 2005

SP - 233

EP - 241

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

SN - 1687-1820

IS - 2

ER -