ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS APPROACH TO MINIMIZATION PROBLEMS

被引：3

作者：

Yao, Yonghong ^{[2
]}

Liou, Y. C. ^{[3
]}

Wong, M. M. ^{[1
]}

机构：

[1] Chung Yuan Christian Univ, Dept Appl Math, Chungli 32023, Taiwan

[2] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

[3] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2010年 / 14卷 / 05期

关键词：

Nonexpansive mapping; Fixed point; Inverse-strongly monotone mapping; Equilibrium problem; Minimum norm; STRONG-CONVERGENCE THEOREM; STEEPEST-DESCENT METHODS; NONEXPANSIVE-MAPPINGS; EXTRAGRADIENT METHOD; VISCOSITY APPROXIMATION; ITERATIVE SCHEME;

D O I：

10.11650/twjm/1500406033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce two algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Furthermore, we prove that the proposed algorithms converge strongly to a solution of the minimization problem of finding x* is an element of Gamma such that parallel to x*parallel to = min(x is an element of Gamma) parallel to x parallel to where Gamma stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping.

引用

页码：2073 / 2089

页数：17

共 29 条

[11]

Moudafi A, 2008, J NONLINEAR CONVEX A, V9, P37

[12] 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

[13] A new hybrid-extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems [J].

Peng, Jian-Wen ;

Yao, Jen-Chih .

TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (06) :1401-1432

[14] Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems [J].

Peng, Jian-Wen ;

Yao, Jen-Chih .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 49 (9-10) :1816-1828

[15]

PENG JW, 2009, TAIWANESE J IN PRESS

[16] Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings [J].

Petrusel, A. ;

Yao, J. -C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (04) :1100-1111

[17] Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals [J].

Suzuki, T .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 305 (01) :227-239

[18] Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space [J].

Takahashi, Satoru ;

Takahashi, Wataru .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (03) :1025-1033

[19] Weak convergence theorems for nonexpansive mappings and monotone mappings [J].

Takahashi, W ;

Toyoda, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 118 (02) :417-428

[20] Convergence of hybrid steepest-descent methods for variational inequalities [J].

Xu, HK ;

Kim, TH .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 119 (01) :185-201

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