A parallel extragradient-like projection method for unrelated variational inequalities and fixed point problems

In this paper, we introduce a parallel extragradient-like projection algorithm for finding a common solution of a system of unrelated variational inequalities and fixed point problems corresponding to different feasible domains in a real Hilbert space. The main idea of the paper, based on the 2006 hybrid extragradient method of Nadezhkina and Takahashi, is to combine three methods including the extragradient method, the Mann iteration method and the projection method with the parallel splitting-up technique. After computing the parallel extragradient iteration point, the next iteration point is modified by projecting a given initial point on the intersect of suitable convex sets to get a strong convergence property under certain assumptions by suitable choice parameters. Finally, a numerical example is developed to illustrate the behavior of our algorithm.