Inertial approximation method for finite families of split monotone inclusion and fixed point problems of certain nonlinear mappings

Abstract

In this paper, we introduce an inertial forward-backward splitting method together with a viscosity iterative algorithm for approximating a common solution of a system of split monotone variational inclusion problem and fixed point problem of finite family of multivalued demicontractive mappings in Hilbert spaces. Under suitable condi-tions, we proved that the sequence generated by our algorithm converges strongly to a solution of the aforementioned problems. We display some numerical experiments to show the behaviour of our result. The result presented in this paper complement and extend many recent results in literature.