Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces

被引：47

作者：

Fan, Jianghua ^{[1
]}

Liu, Xiang

Li, Jinlu ^{[2
]}

机构：

[1] Guangxi Normal Univ, Dept Math, Guilin 541004, Guangxi, Peoples R China

[2] Shawnee State Univ, Dept Math Sci, Portsmouth, OH 45662 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 11期

关键词：

Variational inequality; Generalized projection operator; Iterative schemes; F-PROJECTION OPERATOR; MANN; ISHIKAWA; ALGORITHMS; EXISTENCE; EQUATIONS;

D O I：

10.1016/j.na.2008.08.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce two iterative schemes for approximating solutions of generalized variational inequalities in the setting of Banach spaces. The existence of solutions of this general problem and the convergence of the proposed iterative schemes to a solution are established. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：3997 / 4007

页数：11

共 19 条

[1]

Alber Y., 2001, Analysis, V21, P17, DOI DOI 10.1524/ANLY.2001.21.1.17

[2]

Alber Y.I., 1996, LECT NOTES PURE APPL, P15

[3] On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces [J].

Chang, SS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 216 (01) :94-111

[4] Iterative solutions of nonlinear equations in smooth Banach spaces [J].

Chidume, CE .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (11) :1823-1834

[5]

Chidume CE., 2005, PanAmer. Math. J, V15, P29

[6] A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces [J].

Fan Jianghua .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (02) :1041-1047

[7] Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions [J].

Huang, NJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (10) :1-7

[8]

Kamimura SJ, 2003, SIAM J OPTIMIZ, V13, P938

[9] Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions [J].

Kazmi, KR .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 209 (02) :572-584

[10] An approximation of solutions of variational inequalities [J].

Li, Jinlu ;

Rhoades, B. E. .

FIXED POINT THEORY AND APPLICATIONS, 2005, 2005 (03) :377-388

← 1 2 →