A modified forward-backward splitting method for sum of monotone operators and demicontractive mappings

In this paper, by using a modified forward-backward splitting method, the author introduces and studies an iterative algorithm for finding a common element of the set of fixed points of demicontractive mappings and the set of solutions of variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in real Hilbert spaces. The author proves that the sequence xn which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, some applications are given.