Weak convergence theorem for variational inequality problems with monotone mapping in Hilbert space

Abstract

Abstract We know that variational inequality problem is very important in the nonlinear analysis. The main purpose of this paper is to propose an iterative method for finding an element of the set of solutions of a variational inequality problem with a monotone and Lipschitz continuous mapping in Hilbert space. This iterative method is based on the extragradient method. We get a weak convergence theorem. Using this result, we obtain three weak convergence theorems for the equilibrium problem, the constrained convex minimization problem, and the split feasibility problem.

Keywords

• iterative method
• extragradient method
• weak convergence
• variational inequality
• monotone mapping
• equilibrium problem