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
收藏
页数：21
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