We propose a modified extragradient method for solving the variational inequality problem in Hilbert space. The is combination of well-known subgradient with Mann’s mean value which updated iterate picked convex hull all previous iterates. show weak convergence to solution problem, provided that condition on corresponding averaging matrix fulfilled. Some numerical experiments are given effectiv...

In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...

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 approxi...