Implicit Iteration Scheme with Perturbed Mapping for Equilibrium Problems and Fixed Point Problems of Finitely Many Nonexpansive Mappings

L. C. Ceng (), S. Schaible and J. C. Yao ()
Additional contact information
L. C. Ceng: Shanghai Normal University
S. Schaible: University of California
J. C. Yao: National Sun Yat-Sen University

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 13, 403-418

Abstract: Abstract We introduce an implicit iteration scheme with a perturbed mapping for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. Then, we establish some convergence theorems for this implicit iteration scheme which are connected with results by Xu and Ori (Numer. Funct. Analysis Optim. 22:767–772, 2001), Zeng and Yao (Nonlinear Analysis, Theory, Methods Appl. 64:2507–2515, 2006) and Takahashi and Takahashi (J. Math. Analysis Appl. 331:506–515, 2007). In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained.

Keywords: Implicit iteration scheme with a perturbed mapping; Equilibrium problem; Common fixed point; Finitely many nonexpansive mappings (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9361-y

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