SYSTEMS OF VARIATIONAL INEQUALITIES WITH HIERARCHICAL VARIATIONAL INEQUALITY CONSTRAINTS FOR LIPSCHITZIAN PSEUDOCONTRACTIONS

被引：123

作者：

Ceng, Lu-Chuan ^{[1
]}

Petrusel, Adrian ^{[2
]}

Yao, Jen-Chih ^{[3
,4
]}

Yao, Yonghong ^{[5
,6
]}

机构：

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

[2] Babes Bolyai Univ, Dept Math, Kogalniceanu Str 1, Cluj Napoca 400084, Romania

[3] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan

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

[5] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China

[6] North Minzu Univ, Sch Math & Informat Sci, Yinchuan 750021, Peoples R China

来源：

FIXED POINT THEORY | 2019年 / 20卷 / 01期

关键词：

Implicit composite extragradient-like method; general system of variational inequalities; fixed point; accretive operator; uniform convexity; uniform smoothness; VISCOSITY APPROXIMATION METHODS; FIXED-POINT PROBLEMS; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; PROJECTION METHODS; GENERAL SYSTEM; THEOREMS; ALGORITHMS; IMPLICIT; FAMILY;

D O I：

10.24193/fpt-ro.2019.1.07

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space. We propose an implicit composite extragradient-like method based on the Mann iteration method, the viscosity approximation method and the Korpelevich extragradient method. Convergence results for the proposed iteration method are also established under some suitable assumptions.

引用

页码：113 / 133

页数：21

共 37 条

[1]

Ansari Q. H., 2015, J INEQUAL APPL, V2015

[2] A fixed point theorem and its applications to a system of variational inequalities [J].

Ansari, QH ;

Yao, JC .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1999, 59 (03) :433-442

[3]

ANSARI QH, 2000, APPL ANAL, V76, P203

[4] Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space [J].

Aoyama, Koji ;

Kimura, Yasunori ;

Takahashi, Wataru ;

Toyoda, Masashi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (08) :2350-2360

[5] 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

[6]

Ceng LC, 2015, J NONLINEAR CONVEX A, V16, P385

[7] 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

[8] Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators [J].

Ceng, Lu-Chuan ;

Xu, Hong-Kun .

TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (03) :661-682

[9] Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces [J].

Ceng, Lu-Chuan ;

Liou, Yeong-Cheng ;

Wen, Ching-Fen .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (06) :3136-3154

[10] Three-step Mann iterations for a general system of variational inequalities and an infinite family of nonexpansive mappings in Banach spaces [J].

Ceng, Lu-Chuan ;

Wen, Ching-Feng .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,

← 1 2 3 4 →