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

Chih-Sheng Chuang (), Lai-Jiu Lin () and Wataru Takahashi ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1601 pages

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 (Nonlinear Anal 73:1562–1568, 2010 ) concerning Halpern’s iterations. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Quasi-non expansive mapping; Equilibrium problem; Perturbation; 47H05; 47H09; 47H20 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9911-6

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