Strong Convergence for Generalized Equilibrium Problems, Fixed Point Problems and Relaxed Cocoercive Variational Inequalities

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

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...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

A New System of Generalized Nonlinear Relaxed Cocoercive Variational Inequalities

We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the converg...

Strong Convergence Theorems Based on a New Modified Extragradient Methods for Finite Generalized Ky Fan Inequalities,variational Inequality Problems and Fixed Point Problems

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of finite generalized Ky Fan inequalities and the set of solutions of more general variational inequality for finite relaxed cocoercive operators and the set of common fixed points of a nonexpansive semigroup in Hilbert space. The results obtained in this paper improve and extend the resul...