Iterative procedure with inertial term for the approximation of xed point of strictly pseudo-contractive mapping with application to monotone variational inclusion problems in Hilbert spaces

Resum

Motivated by the recent result in [1], it is our aim in this paper to introduce the modified Mann-type iterative procedure with inertial term for the approximation of fixed point of strictly pseudo-contractive mappings defined on a closed and convex subset of real Hilbert spaces. We prove strong convergence theorem for it. Furthermore, we apply our procedure to the approximation of monotone variational inclusion and variational inequality problems in real Hilbert spaces. In addition, we provide a numerical example to illustrate the effectiveness of our procedure. It is intended that our procedure complement our motivated result cited in the literature.