System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications

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

Variational inequalities on Hilbert $C^*$-modules

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

Three Step Algorithms for Solving Extended General Variational Inequalities

In this paper, we consider extended general variational inequalities involving nonlinear operators. Using projection operator technique, we show that extended general variational inequality is equivalent to a fixed point problem. Using this alternative equivalent formulation, we propose and analyze some new algorithms for solving extended general variational inequalities and its variant forms. ...

Nonlinear Variational Inequalities for Pseudomonotone Operators with Applications∗

In this paper, we prove the existence of solutions to the variational and variational-like inequalities for pseudomonotone and pseudodissipative and, ηpseudomonotone and η-pseudodissipative operators, respectively. As applications of our results, we prove the existence of a unique solution of nonlinear equations, fixed point problems and eigenvalue problems. 1991 Mathematics Subject Classificat...

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...