A Perturbed Iterative Method for a General Class of Variational Inequalities

The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors

We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several exi...

Projection Iterative Approximations for a New Class of General Random Implicit Quasi-variational Inequalities

We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stabi...

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...

Generalized Nonlinear Mixed Quasi-variational Inequalities Involving Maximal Η-monotone Mappings

In this paper, we introduce and study a new class of generalized nonlinear mixed quasi-variational inequalities involving maximal η-monotone mapping. Using the resolvent operator technique for maximal η-monotone mapping, we prove the existence of solution for this kind of generalized nonlinear multi-valued mixed quasi-variational inequalities without compactness and the convergence of iterative...

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