Hybrid iterative algorithms for two families of finite maximal monotone mappings

Fixexd point theory and applications

Jin-Zuo Chen¹  Yang-Qing Qiu¹  Hui-Ying Hu¹  Lu-Chuan Ceng¹ 

[1] Department of Mathematics, Shanghai Normal University, Shanghai, China

关键词: hybrid iterative algorithms;    maximal monotone mappings;    fixed points;    strong convergence;    47H05;    47H10;    47J25;    49J40;   

DOI  :  10.1186/s13663-015-0428-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce and analyze a new general hybrid iterative algorithm for finding a common element of the set of common zeros of two families of finite maximal monotone mappings, the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space. Our algorithm is based on four well-known methods: Mann’s iteration method, composite method, outer-approximation method and extragradient method. We prove the strong convergence theorem for the proposed algorithm. The results presented in this paper extend and improve the corresponding results of Wei and Tan (Fixed Point Theory Appl. 2014:77, 2014). Some special cases are also discussed.

【 授权许可】

CC BY