Finding Common Solutions of a Variational Inequality, a General System of Variational Inequalities, and a Fixed-Point Problem via a Hybrid Extragradient Method

We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type iteration method. By constrasting with other methods, our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined. Furthermore, under mild conditions imposed on the parameters we show that our algorithm generates iterates which converge strongly to a common element of these three problems.