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

被引：0
作者：
L. C. Ceng
S. Schaible
J. C. Yao
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] Scientific Computing Key Laboratory of Shanghai Universities,A.G. Anderson Graduate School of Management
[3] University of California,Department of Applied Mathematics
[4] National Sun Yat-Sen University,undefined
来源：
Journal of Optimization Theory and Applications | 2008年 / 139卷
关键词：
Implicit iteration scheme with a perturbed mapping; Equilibrium problem; Common fixed point; Finitely many nonexpansive mappings;
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学科分类号：
摘要：
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.
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页码：403 / 418
页数：15
相关论文
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