Extra-gradient methods for solving split feasibility and fixed point problems

被引：21

作者：

Chen, Jin-Zuo ^{[1
]}

Ceng, Lu-Chuan ^{[1
]}

Qiu, Yang-Qing ^{[1
]}

Kong, Zhao-Rong ^{[2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Shanghai Univ Polit Sci & Law, Sch Econ & Management, Shanghai, Peoples R China

来源：

FIXED POINT THEORY AND APPLICATIONS | 2015年

关键词：

Ishikawa-type iterative algorithm; Mann-type iterative algorithm; extra-gradient methods; split feasibility problems; fixed point problems; pseudo-contractive mappings; VARIATIONAL-INEQUALITIES; EXTRAGRADIENT METHOD; STRONG-CONVERGENCE; CQ ALGORITHM; SETS; PROJECTION;

D O I：

10.1186/s13663-015-0441-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study the extra-gradient methods for solving split feasibility and fixed point problems involved in pseudo-contractive mappings in real Hilbert spaces. We propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings with Lipschitz assumption. Moreover, we also suggest a Mann-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings without Lipschitz assumption. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility and fixed point problems. The results presented in this paper extend and improve some corresponding ones in the literature.

引用

页数：21

共 50 条

[31] A fixed point method for solving a split feasibility problem in Hilbert spaces [J].

Qin, Xiaolong ;

Wang, Lin .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (01) :315-325

[32] Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings [J].

Jailoka, Pachara ;

Suantai, Suthep .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (05)

[33] A gradient projection method for solving split equality and split feasibility problems in Hilbert spaces [J].

Phan Tu Vuong ;

Strodiot, Jean Jacques ;

Van Hien Nguyen .

OPTIMIZATION, 2015, 64 (11) :2321-2341

[34] HYBRID EXTRAGRADIENT METHODS FOR FINDING MINIMUM-NORM SOLUTIONS OF SPLIT FEASIBILITY PROBLEMS [J].

Ceng, Lu-Chuan ;

Wong, Ngai-Ching ;

Yao, Jen-Chih .

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2015, 16 (10) :1965-1983

[35] Mann's type extragradient for solving split feasibility and fixed point problems of Lipschitz asymptotically quasi-nonexpansive mappings [J].

Deepho, Jitsupa ;

Kumam, Poom .

FIXED POINT THEORY AND APPLICATIONS, 2013,

[36] Mann’s type extragradient for solving split feasibility and fixed point problems of Lipschitz asymptotically quasi-nonexpansive mappings [J].

Jitsupa Deepho ;

Poom Kumam .

Fixed Point Theory and Applications, 2013

[37] APPROXIMATION OF COMMON SOLUTIONS TO PROXIMAL SPLIT FEASIBILITY PROBLEMS AND FIXED POINT PROBLEMS [J].

Shehu, Yekini .

FIXED POINT THEORY, 2017, 18 (01) :361-374

[38] The common solutions of the split feasibility problems and fixed point problems [J].

Abdelouahed Hamdi ;

Yeong-Cheng Liou ;

Yonghong Yao ;

Chongyang Luo .

Journal of Inequalities and Applications, 2015

[39] Dynamic stepsize iteration process for solving split common fixed point problems with applications [J].

Kumar, Ajay ;

Thakur, Balwant Singh ;

Postolache, Mihai .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 218 :498-511

[40] A damped algorithm for the split feasibility and fixed point problems [J].

Li, Cun-lin ;

Liou, Yeong-Cheng ;

Yao, Yonghong .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,

← 1 2 3 4 5 →