An implicit iterative scheme for monotone variational inequalities and fixed point problems

被引：24

作者：

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

Cubiotti, R. ^{[2
]}

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

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] Univ Messina, Dept Math, I-98166 Messina, Italy

[3] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 08期

关键词：

variational inequality; nonexpansive mapping; implicit iterative scheme; monotone mapping; fixed point; weak convergence; demiclosedness principle; opial's condition;

D O I：

10.1016/j.na.2007.08.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce an implicit iterative scheme for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The implicit iterative scheme is based on two well-known methods: extragradient and approximate proximal. We obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme. On the basis of this theorem, we also construct an implicit iterative process for finding a common fixed point of N + 1 mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other N mappings are nonexpansive. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：2445 / 2457

页数：13

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