An inertial iterative method for common solution of a pair of variational inequality problems

In this paper, we have presented a novel inertial-viscosity approximation technique for finding the common element (CE) of solution set of two variational inequality problems in the real Hilbert spaces. First, we investigate the CE of the set of fixed points (FPs) of two Nonexpansive (NE) mappings and then apply our result to find the CE of the solution set of two variational inequality problems. We also discussed on the strong convergence of the proposed algorithm under some moderate circumstances. Our result improves, extends and generalizes some published results in this direction. Furthermore, our results are supported by some numerical examples.