Parallel Algorithms for Solving a Class of Variational Inequalities over the Common Fixed Points Set of a Finite Family of Demicontractive Mappings

Abstract

We propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem.