A strong convergence theorem for relatively nonexpansive mappings in a Banach space

In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert space and maximal mon...

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Bibliographic Details
Published inJournal of approximation theory Vol. 134; no. 2; pp. 257 - 266
Main Authors Matsushita, Shin-ya, Takahashi, Wataru
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2005
Subjects
Asymptotic fixed point
Generalized projection
Maximal monotone operator
Nonexpansive mapping
Relatively nonexpansive mapping
Relatively nonexpansive mapping
Generalized projection
primary 47H09
Asymptotic fixed point
Maximal monotone operator
secondary 47H05
Nonexpansive mapping
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Summary:In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert space and maximal monotone operators in a Banach space.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2005.02.007