Convergence analysis for variational inequality problems and fixed point problems in 2-uniformly smooth and uniformly convex Banach spaces

被引：25

作者：

Cai, Gang ^{[1
]}

Bu, Shangquan ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2012年 / 55卷 / 3-4期

关键词：

Strong convergence; Variational inequality; Fixed point; Nonexpansive mappings; Banach space; NONEXPANSIVE-MAPPINGS; ITERATIVE METHODS; APPROXIMATION; THEOREMS;

D O I：

10.1016/j.mcm.2011.08.031

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we study a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of variational inequalities for two inverse strongly accretive mappings and the set of common fixed points of an infinite family of nonexpansive mappings in a real 2-uniformly smooth and uniformly convex Banach space. We prove some strong convergence theorems under suitable conditions. The results obtained in this paper improve and extend the corresponding results announced by many others. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：538 / 546

页数：9

共 15 条

[11] INEQUALITIES IN BANACH-SPACES WITH APPLICATIONS [J].

XU, HK .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1991, 16 (12) :1127-1138

[12] On viscosity iterative methods for variational inequalities [J].

Yao, Yonghong ;

Noor, Muhammad Aslam .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (02) :776-787

[13] Strong convergence of an iterative algorithm for variational inequalities in Banach spaces [J].

Yao, Yonghong ;

Maruster, Stefan .

MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (1-2) :325-329

[14] Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces [J].

Yao, Yonghong ;

Noor, Muhammad Aslam ;

Noor, Khalida Inayat ;

Liou, Yeong-Cheng ;

Yaqoob, Huma .

ACTA APPLICANDAE MATHEMATICAE, 2010, 110 (03) :1211-1224

[15] Convergence theorems for fixed point problems and variational inequality problems in Hilbert spaces [J].

Yao, Yonghong ;

Liou, Yeong-Cheng ;

Chen, Rudong .

MATHEMATISCHE NACHRICHTEN, 2009, 282 (12) :1827-1835

← 1 2 →