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

Abstract

Abstract 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.

Keywords

• variational inequality problem
• fixed point problems; monotone mapping
• nonexpansive mapping
• extragradient method
• <it>CQ </it>method
• projection