A general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces

Fixexd point theory and applications

Cuijie Zhang¹  Songnian He¹ 

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

关键词: an infinite family of nonexpansive operators;    strong convergence;    k-Lipschitizian;    η-strongly monotone;    split common fixed point problem;   

DOI  :  10.1186/1687-1812-2013-138

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a new general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to a common point of the sets of fixed points, which solves a variational inequality. Our results improve and extend the corresponding results announced by many others. As applications, at the end of the paper, we apply our results to the split common fixed point problem.

【 授权许可】

CC BY