The solvability on a new system of nonlinear variational inclusions in Hilbert spaces

In order to study the solvability on a new system of nonlinear variational inclusions in Hilbert Spaces, the operators involving three classes of (K,η) are proposed in the paper, and a new algorithm for solutions of this system is constructed. The approximation solvability for the system of generalized nonlinear variational inclusions is discussed by using the resolvent operator technique in a Hilbert setting. For showing the existence of solutions of the system, a three-step iterative scheme with errors is adopted. Furthermore, a convergence result of the sequences generated by the algorithm is considered.