Published in

SpringerOpen, Journal of Inequalities and Applications, 1(2016)

DOI: 10.1186/s13660-016-1237-3

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

Journal article published in 2016 by Ming Tian, Bing-Nan Jiang
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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. MSC: 58E35, 47H09, 65J15.