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JGO
2010

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

10 years 2 months ago
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.
Lu-Chuan Ceng, Nicolas Hadjisavvas, Ngai-Ching Won
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JGO
Authors Lu-Chuan Ceng, Nicolas Hadjisavvas, Ngai-Ching Wong
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