Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces

In this paper, we introduce a new general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general variational inequality for two inverse-strongly accretive mappings in Banach space. We obt...

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Bibliographic Details
Published inJournal of global optimization Vol. 55; no. 2; pp. 437 - 457
Main Authors Cai, Gang, Bu, Shangquan
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.02.2013
Springer
Springer Nature B.V
Subjects
Algorithms
Banach space
Banach spaces
Computer Science
Convergence
Fixed points (mathematics)
Hilbert space
Inequalities
Iterative algorithms
Iterative methods
Mapping
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Theorems
Strong convergence
47H10
Variational inequality
47H09
Banach space
Nonexpansive mapping
Fixed point
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Summary:In this paper, we introduce a new general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general variational inequality for two inverse-strongly accretive mappings in Banach space. We obtain some strong convergence theorems by a modified extragradient method under suitable conditions. Our results extend the recent results announced by many others.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9883-6