Strong convergence theorems by a hybrid extragradient-like approximation method for asymptotically nonexpansive mappings in the intermediate sense in Hilbert spaces
Eskandar Naraghirad, Ngai‐Ching Wong, Jen‐Chih Yao · Journal of Inequalities and Applications · 2011
Abstract Let C be a nonempty closed convex subset of a real Hilbert space H. Let S : C → C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F(S). Let A : C → H be a Lipschitz continuous map, and VI(C, A) be the set of solutions u ∈ C of the variational inequality ⟨ A u , v - u ⟩ ≥ 0 , ∀ v ∈ C . The purpose of this study is to introduce a hybrid extragradient-like approximation method for finding a common element in F(S) and VI(C, A). We establish some strong convergence theorems for sequences produced by our iterative method. AMS subject classifications: 49J25; 47H05; 47H09.