Halpern’s type iterations with perturbations in Hilbert spaces: equilibrium solutions and fixed points

In this paper, we consider an iteration process of Halpern’s type for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points for a quasi-nonexpansive mapping with perturbation in a Hilbert space and then prove a strong convergence theorem for such iter...

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Bibliographic Details
Published in:Journal of global optimization Vol. 56; no. 4; pp. 1591 - 1601
Main Authors: Chuang, Chih-Sheng, Lin, Lai-Jiu, Takahashi, Wataru
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2013
Springer
Springer Nature B.V
Subjects:
Banach spaces
Codes
Computer Science
Convergence
Equilibrium
Fixed points (mathematics)
Hilbert space
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Operations Research/Decision Theory
Optimization
Perturbation
Real Functions
Studies
Theorems
47H09
Quasi-non expansive mapping
Perturbation
Equilibrium problem
47H05
47H20
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we consider an iteration process of Halpern’s type for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points for a quasi-nonexpansive mapping with perturbation in a Hilbert space and then prove a strong convergence theorem for such iterations. Using this result, we obtain new strong convergence theorems in a Hilbert space. In particular, we solve partially an open problem posed by Kurokawa and Takahashi (Nonlinear Anal 73:1562–1568, 2010 ) concerning Halpern’s iterations.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9911-6