A New System of Generalized Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Spaces

In this paper, we first introduce a new system of generalized variational inequalities involving relaxed cocoercive mappings in Hilbert space. By using the projection method, we prove the existence and uniqueness of solutions for this new system of generalized variational inequalities. We also construct a new algorithm for approximating the solution of this system. The results presented in this paper extend and improve many related results.