Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. The...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2013-11, Vol.159 (2), p.399-411
Main Authors: Buong, Nguyen, Phuong, Nguyen Thi Hong
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Banach space
Banach spaces
Calculus of Variations and Optimal Control
Optimization
Convergence
Engineering
Gateaux
Hilbert space
Inequalities
Mapping
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Norms
Operations Research/Decision Theory
Optimization
Optimization algorithms
Studies
Theory of Computation
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Summary:In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V -mappings instead of W -ones.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0350-4