Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 331, Issue 1, Pages 506-515Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2006.08.036
Keywords
viscosity approximation method; equilibrium problem; fixed point; nonexpansive mapping
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In this paper, we introduce 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. Then, we prove a strong convergence theorem which is connected with Combettes and Hirstoaga's result [PL. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 117-136] and Wittmann's result [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. Using this result, we obtain two corollaries which improve and extend their results. (C) 2006 Elsevier Inc. All rights reserved.
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