General System of A-Monotone Nonlinear Variational Inclusions Problems with Applications

Abstract

We introduce and study a new system of nonlinear variational inclusions involving a combination of A-Monotone operators and relaxed cocoercive mappings. By using the resolvent technique of the A-monotone operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions. The results in this paper unify, extend, and improve some known results in literature.