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

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

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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: , ,
Keywords: iterative methods, perturbation analysis, Hilbert space, fixed point theory
Abstract:

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.

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