Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point prob

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F(S) of a nonexpansive mapping S and the set of solutions ΩA of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approximation) method. The method produces three sequences which are shown to converge strongly to the same common element of F(S) ∩ ΩA. As applications, the method provides an algorithm for finding the common fixed point of a nonexpansive mapping and a pseudocontractive mapping, or a common zero of a monotone Lipschitz continuous mapping and a maximal monotone mapping.

• Type: Journal
• Year: 2010
• Where: JGO
• Authors: Lu-Chuan Ceng, Nicolas Hadjisavvas, Ngai-Ching Wong
• Keywords: Common Element, Continuous Mapping, JGO 2010, Nonexpansive Mapping