A note on “Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings”

In [C.O. Chidume, G. De Souza, Convergence of a Halpern-type iteration algorithm for a class of pseudocontractive mappings, Nonlinear Analysis (2007), doi:10.1016/j.na.2007.08.008], the authors proved a strong convergence result for strictly pseudo-contractive mappings using a Halpern-type iteration...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 70; no. 7; pp. 2519 - 2520
Main Author: Su, Yongfu
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.04.2009
Elsevier
Subjects:
Exact sciences and technology
Fixed point
Global analysis, analysis on manifolds
Halpern iteration
Mathematical analysis
Mathematics
Pseudo-contractive mapping
Sciences and techniques of general use
Strong convergence
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
47H09
Halpern iteration
47H10
Strong convergence
Pseudo-contractive mapping
Fixed point
Fix point
Nonlinear analysis
Iteration
Mathematical model
Algorithm
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary:In [C.O. Chidume, G. De Souza, Convergence of a Halpern-type iteration algorithm for a class of pseudocontractive mappings, Nonlinear Analysis (2007), doi:10.1016/j.na.2007.08.008], the authors proved a strong convergence result for strictly pseudo-contractive mappings using a Halpern-type iteration algorithm. However, the main result is not correct. In this note, we provide a counter-example to the theorem.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.03.036