a relaxed extra gradient approximation method of two inverse-strongly monotone mappings for a general system of variational inequalities, fixed point and equilibrium problems

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Viscosity Approximation Methods for Equilibrium Problems and Fixed Point Problems of Nonexpansive Mappings and Inverse-strongly Monotone Mappings∗

In this paper, we introduce an iterative scheme by viscosity approximation method for obtaining a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. We obtain a strong convergence which improves and extends S. Tak...

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 ...

Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studi...

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 ...

Monotone variational inequalities, generalized equilibrium problems and fixed point methods

In this paper, we study monotone variational inequalities and generalized equilibrium problems. Weak convergence theorems are established based on a fixed point method in the framework of Hilbert spaces.