Strong convergence of a hybrid projection iterative algorithm for common solutions of operator equations and of inclusion problems

被引：15

作者：

Wu, Changqun ^{[1
]}

Liu, Aichao ^{[2
]}

机构：

[1] Henan Univ, Sch Business & Adm, Kaifeng 45000, Peoples R China

[2] Huanghuai Univ, Dept Math, Zhumadian 463000, Peoples R China

来源：

FIXED POINT THEORY AND APPLICATIONS | 2012年

关键词：

fixed point; monotone operator; strict pseudocontraction; variational inequality; zero point; GENERALIZED EQUILIBRIUM PROBLEMS; VARIATIONAL INEQUALITY PROBLEM; FIXED-POINT PROBLEMS; NONEXPANSIVE-MAPPINGS; WEAK-CONVERGENCE; THEOREMS; SUMS;

D O I：

10.1186/1687-1812-2012-90

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, zero points of the sum of a maximal monotone operator and an inverse-strongly monotone mapping, solutions of a monotone variational inequality, and fixed points of a strict pseudocontraction are investigated. A hybrid projection iterative algorithm is considered for analyzing the convergence of the iterative sequences. Strong convergence theorems are established in the framework of real Hilbert spaces without any compact assumptions. Some applications of the main results are also provided. AMS Classification: 47H05; 47H09; 47J25; 90C33.

引用

页数：15

共 53 条

[41] Enlargements and sums of monotone operators [J].

Revalski, JP ;

Théra, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 48 (04) :505-519

[42] ON MAXIMALITY OF SUMS OF NONLINEAR MONOTONE OPERATORS [J].

ROCKAFELLAR, RT .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 149 (01) :75-+

[43]

ROCKAFELLAR RT, 1996, PAC J MATH, V17, P497

[44]

Saewan S., 2010, ABSTR APPL ANAL, V22

[45] A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces [J].

Shehu, Yekini .

JOURNAL OF GLOBAL OPTIMIZATION, 2012, 54 (03) :519-535

[46]

Solodov MV, 1999, J CONVEX ANAL, V6, P59

[47] Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces [J].

Takahashi, S. ;

Takahashi, W. ;

Toyoda, M. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2010, 147 (01) :27-41

[48] 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

[49] Critical Size for the Observation of Quantum Confinement in Optically Excited Gold Clusters [J].

Varnavski, Oleg ;

Ramakrishna, Guda ;

Kim, Junhyung ;

Lee, Dongil ;

Goodson, Theodore .

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 2010, 132 (01) :16-+

[50]

Yang S, 2011, ADV FIXED POINT THEO, V1, P15

← 1 2 3 4 5 6 →