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

被引：18

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

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