Parallel projection methods for variational inequalities involving common fixed point problems

Abstract

In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive mappings. A technical extension in the proposed algorithms helps in computing practical numerical experiments when the number of subproblems is large. Some numerical examples are implemented to demonstrate the efficiency of parallel computations.