Article ID: | iaor20134141 |
Volume: | 56 |
Issue: | 4 |
Start Page Number: | 1591 |
End Page Number: | 1601 |
Publication Date: | Aug 2013 |
Journal: | Journal of Global Optimization |
Authors: | Takahashi Wataru, Lin Lai-Jiu, Chuang Chih-Sheng |
Keywords: | iterative methods, perturbation analysis, Hilbert space, fixed point theory |
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 (2010) concerning Halpern’s iterations.