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

Fixexd point theory and applications

Jin-Zuo Chen¹  Yang-Qing Qiu¹  Lu-Chuan Ceng¹  Zhao-Rong Kong² 

[1] Department of Mathematics, Shanghai Normal University, Shanghai, China;School of Economics and Management, Shanghai University of Political Science and Law, Shanghai, China

关键词: Ishikawa-type iterative algorithm;    Mann-type iterative algorithm;    extra-gradient methods;    split feasibility problems;    fixed point problems;    pseudo-contractive mappings;    47J25;    47H09;    47H10;    65J15;   

DOI  :  10.1186/s13663-015-0441-z

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY