Perturbed Mann iterative method with errors for a new system of generalized nonlinear variational-like inclusions

In this paper, a new system of generalized nonlinear variational-like inclusions is introduced and investigated in Hilbert spaces. By means of the resolvent operator technique, the existence and uniqueness of solution for the system of generalized nonlinear variational-like inclusions is demonstrated. Moreover, a perturbed Mann iterative method with errors for approximating the solution of the system of generalized nonlinear variational-like inclusions is constructed and the convergence and stability of the iterative sequence generated by the algorithm is discussed. The results presented in this paper generalize and unify many known results in the literature.