An explicit projection method for a system of nonlinear variational inequalities with different (γ,r)-cocoercive mappings

In this paper, we introduce and consider a new system of variational inequalities involving two different operators. Using the projection technique, we suggest and analyze new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.