A Totally Relaxed, Self-Adaptive Subgradient Extragradient Method for Variational Inequality and Fixed Point Problems in a Banach Space

Convergence Analysis of a Hybrid Relaxed-Extragradient Method for Monotone Variational Inequalities and Fixed Point Problems

In this paper we introduce a hybrid relaxed-extragradient method for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The hybrid relaxed-extragradient method is based on two well-known methods: hybrid and extragradient. We derive a strong convergence ...

A Viscosity Relaxed–extragradient Method for Monotone Variational Inequalities and Fixed Point Problems

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 ...

An Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...

Research Article An Extragradient Method for Fixed Point Problems and Variational Inequality Problems

An extragradient-like approximation method for variational inequality problems and fixed point problems

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish...