A modified halpern-type iteration algorithm for totally quasi- ϕ-asymptotically nonexpansive mappings with applications

The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi- ϕ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding...

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Published in:Applied mathematics and computation Vol. 218; no. 11; pp. 6489 - 6497
Main Authors: Chang, S.S., Joseph Lee, H.W., Chan, Chi Kin, Zhang, W.B.
Format: Journal Article
Language:English
Published: Elsevier Inc 05.02.2012
Subjects:
Algorithms
Banach space
Computation
Convergence
Generalized projection
Halpern-type iteration algorithm
Iterative methods
Mapping
Mathematical models
Nonexpansive mapping
Nonlinearity
Quasi- ϕ-nonexpansive mapping
Quasi- ϕ-symptotically nonexpansive mapping
Relatively nonexpansive mapping
Total quasi- ϕ-symptotically nonexpansive mapping
Weak relatively nonexpansive mapping
Halpern-type iteration algorithm
Quasi- ϕ-symptotically nonexpansive mapping
Total quasi- ϕ-symptotically nonexpansive mapping
Relatively nonexpansive mapping
Generalized projection
Weak relatively nonexpansive mapping
Quasi- ϕ-nonexpansive mapping
Nonexpansive mapping
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi- ϕ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi- ϕ-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051–1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364–2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400–2411] and others.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.12.019