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 $x_n$ which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, some applications are given.