Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2011; no. 1; pp. 1 - 10
• Main Authors: Yao, Yonghong, Liou, Yeong-Cheng, Wong, Mu-Ming, Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17.09.2011; Springer Nature B.V; BioMed Central Ltd; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Classification; Convergence; CQ method; Differential Geometry; extragradient method; fixed point problems; monotone mapping; Fixed points (mathematics); Inequalities; Iterative methods; Mapping; Mathematical analysis; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; nonexpansive mapping; projection; Sequences; Topology; variational inequality problem; nonexpansive mapping; projection; extragradient method; method; variational inequality problem; fixed point problems; monotone mapping
• ISSN: 1687-1812; 1687-1820; 1687-1812; 2730-5422
• DOI: 10.1186/1687-1812-2011-53

In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.