The modified extragradient method for nonexpansive multivalued mappings and variational inequality problems

In this paper, we prove the strong convergence of an approximating common element of the set of fixed points of a nonexpansive multivalued mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping in a Hilbert space by using the modified extragradient method. As applications, we give the example and numerical results for supporting our main theorem. Keywords: Extragradient method; Variational inequality; Nonexpansive multi-valued mapping; Iteration; Hilbert space.
1 Introduction Let H be a real Hilbert space with inner product [??]*,* [??] and norm [parallel] * [parallel], respectively. Let C be a nonempty closed convex subset of H. [...]