A modified inertial shrinking projection method for solving inclusion problems and quasi-nonexpansive multivalued mappings

In this work, we propose a modified inertial and forward-backward splitting method for solving the fixed point problem of a quasi-nonexpansive multivalued mapping and the inclusion problem. Then, we establish the weak convergence theorem of the proposed method. The strongly convergent theorem is also established under suitable assumptions in Hilbert spaces using the shrinking projection method. Some preliminary numerical experiments are tested to illustrate the advantage performance of our methods.