Strong convergence theorems for the split equality variational inclusion problem and fixed point problem in Hilbert spaces

Fixexd point theory and applications

Rudong Chen¹  Haili Guo¹  Huimin He² 

[1] Department of Mathematics, Tianjin Polytechnic University, Tianjin, China;School of Mathematics and Statistics, Xidian University, Xian, China

关键词: split equality problem;    split equality variational inclusion problem;    fixed point;    variational inequality;   

DOI  :  10.1186/s13663-015-0470-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose and investigate two new iterative algorithms for solving the split equality variational inclusion problem in Hilbert spaces. We also prove that the sequences generated by the proposed algorithms converge strongly to a common solution of the split equality variational inclusion problem and fixed points of a family of nonexpansive mappings, which is also an unique solution of a variational inequality as an optimality condition for a minimization problem. The results presented in this paper extend and generalize a variety of existing results in this area.

【 授权许可】

CC BY