Convergence of Ishikawa's iteration method for pseudocontractive mappings

Habtu Zegeye, Naseer Shahzad, Mohammad A. Alghamdi

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.

Original languageEnglish
Pages (from-to)7304-7311
Number of pages8
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number18
DOIs
Publication statusPublished - Dec 1 2011

Fingerprint

Lipschitz Mapping
Ishikawa Iteration
Pseudocontractive Mapping
Iteration Method
Common Fixed Point
Nonlinear Mapping
Closed set
Strong Convergence
Convex Sets
Compactness
Interior
Hilbert space
Hilbert spaces
Set theory
Closed
Subset
Family
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{2f092d503281488f821a0e6d18548891,
title = "Convergence of Ishikawa's iteration method for pseudocontractive mappings",
abstract = "Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.",
author = "Habtu Zegeye and Naseer Shahzad and Alghamdi, {Mohammad A.}",
year = "2011",
month = "12",
day = "1",
doi = "10.1016/j.na.2011.07.048",
language = "English",
volume = "74",
pages = "7304--7311",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "18",

}

Convergence of Ishikawa's iteration method for pseudocontractive mappings. / Zegeye, Habtu; Shahzad, Naseer; Alghamdi, Mohammad A.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 74, No. 18, 01.12.2011, p. 7304-7311.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Convergence of Ishikawa's iteration method for pseudocontractive mappings

AU - Zegeye, Habtu

AU - Shahzad, Naseer

AU - Alghamdi, Mohammad A.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.

AB - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.

UR - http://www.scopus.com/inward/record.url?scp=80052814446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052814446&partnerID=8YFLogxK

U2 - 10.1016/j.na.2011.07.048

DO - 10.1016/j.na.2011.07.048

M3 - Article

VL - 74

SP - 7304

EP - 7311

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 18

ER -