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

[1]

[Anonymous], 1976, P S PURE MATH

[2]

[Anonymous], 1966, COMP MATH MATH PHYS+

[3]

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

[4] NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE [J].

BROWDER, FE .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (04) :1041-&

[5] Enlargement of monotone operators with applications to variational inequalities [J].

Burachik, RS ;

Iusem, AN ;

Svaiter, BF .

SET-VALUED ANALYSIS, 1997, 5 (02) :159-180

[6] ε-Enlargements of maximal monotone operators in Banach spaces [J].

Burachik, RS ;

Svaiter, BF .

SET-VALUED ANALYSIS, 1999, 7 (02) :117-132

[7] A unified treatment of some iterative algorithms in signal processing and image reconstruction [J].

Byrne, C .

INVERSE PROBLEMS, 2004, 20 (01) :103-120

[8] PROJECTED GRADIENT METHODS FOR LINEARLY CONSTRAINED PROBLEMS [J].

CALAMAI, PH ;

MORE, JJ .

MATHEMATICAL PROGRAMMING, 1987, 39 (01) :93-116

[9] The multiple-sets split feasibility problem and its applications for inverse problems [J].

Censor, Y ;

Elfving, T ;

Kopf, N ;

Bortfeld, T .

INVERSE PROBLEMS, 2005, 21 (06) :2071-2084

[10] A unified approach for inversion problems in intensity-modulated radiation therapy [J].

Censor, Yair ;

Bortfeld, Thomas ;

Martin, Benjamin ;

Trofimov, Alexei .

PHYSICS IN MEDICINE AND BIOLOGY, 2006, 51 (10) :2353-2365

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