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.
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Chuang, CS., Lin, LJ. & Takahashi, W. Halpern’s type iterations with perturbations in Hilbert spaces: equilibrium solutions and fixed points. J Glob Optim 56, 1591–1601 (2013). https://doi.org/10.1007/s10898-012-9911-6
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DOI: https://doi.org/10.1007/s10898-012-9911-6