Keywords--Variat ional inequalities, Projection method, Fixed point, Convergence. 1. I N T R O D U C T I O N Variational inequalities.have had a great impact and influence in the development of almost all branches of pure and applied sciences. There are a substantial number of numerical methods including projection, the WieneroHopf equations, auxiliary principle techniques for solving variation...

In this paper, we introduce the extragradient method for finding a common element of the set of solutions of generalized mixed equilibrium problem, the set of common fixed point of family of nonexpansive mappings the set of variational inequality for monotone, Lipschitz continuous mapping in a Hilbert space. Then we prove the strong convergence of iterative algorithm to a common element of this...

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extr...

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving a variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once a...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F (S) of a nonexpansive mapping S and the set of solutions ΩA of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approxi...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion proper...

This paper proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the convergence of the iterative sequences and the range of application of the method is given. Mathematics Subject Classification (2010). 47J20, 49J40, 49M30.

We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi’s hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is pr...