A new explicit iterative algorithm for solving a class of variational inequalities over the common fixed points set of a finite family of nonexpansive mappings

Fixexd point theory and applications

Cuijie Zhang¹  Caiping Yang¹ 

[1] College of Science, Civil Aviation University of China, Tianjin, P.R. China

关键词: nonexpansive mapping;    strong convergence;    variational inequalities;    common fixed points;   

DOI  :  10.1186/1687-1812-2014-60

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a new explicit iterative algorithm for finding a solution for a class of variational inequalities over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the variational inequality. Our result improves and extends the corresponding results announced by many others. At the end of the paper, we extend our result to the more broad family of λ-strictly pseudo-contractive mappings.

【 授权许可】

CC BY