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 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, <CitationRef CitationID="CR10">2010</CitationRef>) concerning Halpern’s iterations. Copyright Springer Science+Business Media, LLC. 2013
Year of publication: |
2013
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Authors: | Chuang, Chih-Sheng ; Lin, Lai-Jiu ; Takahashi, Wataru |
Published in: |
Journal of Global Optimization. - Springer. - Vol. 56.2013, 4, p. 1591-1601
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Publisher: |
Springer |
Subject: | Quasi-non expansive mapping | Equilibrium problem | Perturbation |
Saved in:
Online Resource