Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 198, Issue 2, Pages 729-741Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2007.09.011
Keywords
viscosity approximation method; equilibrium problem; fixed point; nonexpansive mapping
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Recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 2006, doi: 10.1016/j.jmaa.2006.08.036] suggested and analyzed an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, we introduce a new iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space. Then, we prove a strong convergence theorem which is the improvements and extension of Takahashi and Takahashi's (2006) corresponding result. Using this theorem, we obtain two corollaries which improve and extend their corresponding results. (C) 2007 Elsevier Inc. All rights reserved.
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