Strong convergence theorems by a hybrid extragradient-like approximation method for asymptotically nonexpansive mappings in the intermediate sense in Hilbert spaces

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 V I(C,A) be the set of solutions u ∈ C of the variational inequality 〈Au, v − u〉 ≥ 0, ∀v ∈ C. The purpose of this work is to introduce a hybrid extragradient-like approximation method for finding a common element in F (S) and V I(C,A). We establish some strong convergence theorems for sequences produced by our iterative method.