Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces

In this paper, we introduce an ergodic-type method for solving a system of split variational inclusion and fixed point problems of a family of nonexpansive mappings with averaged resolvent operator. We prove that the sequence generated by the proposed algorithm converges strongly to a common element of the set of solutions of a system of split variational inclusion and the set of fixed points of a family of nonexpansive mappings in Hilbert spaces, from which the minimum norm solution is deduced as a special case. Moreover, a numerical example is given to illustrate the operational reliability and convergence of the presented method and results, which may be viewed as a refinement and improvement of the previously known results.