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.
Highlights
The variational inequality problem is a generalization of the nonlinear complementarity problem
In the s, the variational inequality problem became more important in nonlinear analysis
In this paper, based on the extragradient method, we introduce an iterative method for finding an element of the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping in Hilbert space
Summary
The variational inequality problem is a generalization of the nonlinear complementarity problem. It is widely used in economics, engineering, mechanics, signal processing, image processing, and so on. The variational inequality was first derived from the mechanics problems in the early s. In , the existence and uniqueness of solutions of variational inequalities were presented for the first time. Some scientists have published a series of articles. In the s, the variational inequality problem had been used in many fields. In the s, the variational inequality problem became more important in nonlinear analysis
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