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

被引：39

作者：

Ceng, L. C. ^{[2
,3
]}

Schaible, S. ^{[4
]}

Yao, J. C. ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

[2] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China

[3] Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China

[4] Univ Calif Riverside, AG Anderson Grad Sch Management, Riverside, CA 92521 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2008年 / 139卷 / 02期

基金：

美国国家科学基金会;

关键词：

Implicit iteration scheme with a perturbed mapping; Equilibrium problem; Common fixed point; Finitely many nonexpansive mappings;

D O I：

10.1007/s10957-008-9361-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

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.

引用

页码：403 / 418

页数：16

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