Hybrid iterative algorithms for two families of finite maximal monotone mappings

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 probl...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering 2015-10, Vol.2015 (1), p.1-18, Article 180
Main Authors: Qiu, Yang-Qing, Ceng, Lu-Chuan, Chen, Jin-Zuo, Hu, Hui-Ying
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Convergence
Differential Geometry
Hilbert space
Inequalities
Iterative algorithms
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Theorems
Topology
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Summary: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.
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-015-0428-9