Halpern's type iterations with perturbations in Hilbert spaces: equilibrium solutions and fixed points

被引：10

作者：

Chuang, Chih-Sheng ^{[1
]}

Lin, Lai-Jiu ^{[1
]}

Takahashi, Wataru ^{[1
,2
]}

机构：

[1] Natl Changhua Univ Educ, Dept Math, Changhua, Taiwan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2013年 / 56卷 / 04期

关键词：

Quasi-non expansive mapping; Equilibrium problem; Perturbation; STRONG-CONVERGENCE THEOREMS; NONEXPANSIVE-MAPPINGS; NONLINEAR MAPPINGS; HYBRID MAPPINGS; WEAK; APPROXIMATION;

D O I：

10.1007/s10898-012-9911-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we consider an iteration process of Halpern's type for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points for a quasi-nonexpansive mapping with perturbation in a Hilbert space and then prove a strong convergence theorem for such iterations. Using this result, we obtain new strong convergence theorems in a Hilbert space. In particular, we solve partially an open problem posed by Kurokawa and Takahashi (Nonlinear Anal 73:1562-1568, 2010) concerning Halpern's iterations.

引用

页码：1591 / 1601

页数：11

共 22 条

[1] 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

[2]

Aoyama K, 2010, J NONLINEAR CONVEX A, V11, P335

[3]

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

[4]

Combettes PL, 2005, J NONLINEAR CONVEX A, V6, P117

[5] FIXED POINTS OF NONEXPANDING MAPS [J].

HALPERN, B .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (06) :957-&

[6]

Hojo M., 2011, SCI MATH JPN, V73, P31

[7] COMMON FIXED-POINT THEORY OF SINGLEVALUED MAPPINGS AND MULTIVALUED MAPPINGS [J].

ITOH, S ;

TAKAHASHI, W .

PACIFIC JOURNAL OF MATHEMATICS, 1978, 79 (02) :493-508

[8] FIXED POINT THEOREMS AND WEAK CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES [J].

Kocourek, Pavel ;

Takahashi, Wataru ;

Yao, Jen-Chih .

TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (06) :2497-2511

[9] Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces [J].

Kohsaka, Fumiaki ;

Takahashi, Wataru .

ARCHIV DER MATHEMATIK, 2008, 91 (02) :166-177

[10] Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces [J].

Kurokawa, Yu ;

Takahashi, Wataru .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (06) :1562-1568

← 1 2 3 →