A Hybrid Extragradient Method for Solving Ky Fan Inequalities, Variational Inequalities and Fixed Point 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

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 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...

Some Extragradient Methods for Nonconvex Quasi Variational Inequalities (communicated by M.s.moslehian)

In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general nonconvex quasi variational inequalities and the fixed point problems. This alternative equivalent formul...

Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities

‎A new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎Moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...