Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces

In an infinite-dimensional Hilbert space, the normal Mann’s iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann’s iterative process for an infinite family of nonexpansive mappings in the fra...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2009-08, Vol.230 (1), p.121-127
Main Authors: Qin, Xiaolong, Cho, Yeol Je, Kang, Jung Im, Kang, Shin Min
Format: Article
Language:English
Subjects:
Contraction
Exact sciences and technology
Fixed point
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Nonexpansive mapping
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Strong convergence
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In an infinite-dimensional Hilbert space, the normal Mann’s iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann’s iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.10.058