Approximation methods for common solutions of generalized equilibrium, systems of nonlinear variational inequalities and fixed point problems

被引：39

作者：

Cho, Yeol Je ^{[2
,3
]}

Argyros, Loannis K. ^{[4
]}

Petrot, Narin ^{[1
]}

机构：

[1] Naresuan Univ, Fac Sci, Dept Math, Phitsanulok 65000, Thailand

[2] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

[4] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 60卷 / 08期

关键词：

Generalized equilibrium problem; System of nonlinear variational inequalities; Nonexpansive mapping; Strict pseudo-contraction mappings; STRONG-CONVERGENCE THEOREMS; MAPPINGS;

D O I：

10.1016/j.camwa.2010.08.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce an iterative method for finding a common element of the set of solutions of the generalized equilibrium problems, the set of solutions for the systems of nonlinear variational inequalities problems and the set of fixed points of nonexpansive mappings in Hilbert spaces. Furthermore, we apply our main result to the set of fixed points of an infinite family of strict pseudo-contraction mappings. The results obtained in this paper are viewed as a refinement and improvement of the previously known results. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2292 / 2301

页数：10

共 23 条

[1]

Blum E., 1994, Math. Stud., V63, P127

[2]

BROWDER FE, 1967, ARCH RATION MECH AN, V24, P82

[3] PROPERTIES OF FIXED-POINT SETS OF NONEXPANSIVE MAPPINGS IN BANACH SPACES [J].

BRUCK, RE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 179 (MAY) :251-262

[4] Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities [J].

Ceng, Lu-Chuan ;

Wang, Chang-yu ;

Yao, Jen-Chih .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2008, 67 (03) :375-390

[5] Viscosity approximation methods for generalized equilibrium problems and fixed point problems [J].

Ceng, Lu-Chuan ;

Ansari, Qamrul Hasan ;

Yao, Jen-Chih .

JOURNAL OF GLOBAL OPTIMIZATION, 2009, 43 (04) :487-502

[6] A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization [J].

Chang, Shih-sen ;

Lee, H. W. Joseph ;

Chan, Chi Kin .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (09) :3307-3319

[7] SOME REMARKS ON VARIATIONAL-LIKE AND QUASI-VARIATIONAL-LIKE INEQUALITIES [J].

DIEN, NH .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (02) :335-342

[8] Existence theorems for generalized noncoercive equilibrium problems:: The quasi-convex case [J].

Flores-Bazán, F .

SIAM JOURNAL ON OPTIMIZATION, 2001, 11 (03) :675-690

[9]

Noor M. A., 1994, Optimization, V30, P323

[10]

Noor M. A., 1994, Le Math.(Catania), V49, P313

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