An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

被引：14

作者：

Petrusel, Adrian ^{[1
]}

Yao, Jen-Chih ^{[2
]}

机构：

[1] Univ Babes Bolyai, Dept Appl Math, R-3400 Cluj Napoca, Romania

[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2009年 / 7卷 / 02期

关键词：

Modified extragradient method; Viscosity approximation method; Fixed point; alpha-inverse-strongly-monotone mapping; Nonexpansive mapping; Variational inequalities; WEAK-CONVERGENCE THEOREM; NONEXPANSIVE-MAPPINGS; MONOTONE MAPPINGS;

D O I：

10.2478/s11533-009-0003-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an alpha-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.

引用

页码：335 / 347

页数：13

共 17 条

[1] CONSTRUCTION OF FIXED POINTS OF NONLINEAR MAPPINGS IN HILBERT SPACE [J].

BROWDER, FE ;

PETRYSHY.WV .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1967, 20 (02) :197-&

[2]

Ceng LC, 2008, FIXED POINT THEOR-RO, V9, P73

[3] Viscosity approximation methods for nonexpansive mappings and monotone mappings [J].

Chen, Junmin ;

Zhang, Lijuan ;

Fan, Tiegang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (02) :1450-1461

[4]

Korpelevich G., 1976, Matecon, V12, P747

[5] Regularization of nonlinear ill-posed variational inequalities and convergence rates [J].

Liu, FS ;

Nashed, MZ .

SET-VALUED ANALYSIS, 1998, 6 (04) :313-344

[6] Viscosity approximation methods for fixed-points problems [J].

Moudafi, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 241 (01) :46-55

[7] Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings [J].

Nadezhkina, N ;

Takahashi, W .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2006, 128 (01) :191-201

[8] Modified projection method for pseudomonotone variational inequalities [J].

Noor, MA .

APPLIED MATHEMATICS LETTERS, 2002, 15 (03) :315-320

[9] WEAK CONVERGENCE OF SEQUENCE OF SUCCESSIVE APPROXIMATIONS FOR NONEXPANSIVE MAPPINGS [J].

OPIAL, Z .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (04) :591-&

[10]

Peng JW, 2008, FIXED POINT THEOR-RO, V9, P515

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