Weak and strong convergence of inertial algorithms for solving split common fixed point problems

In this paper, we propose two iterative schemes for approximating solutions of split common fixed point problems in multiple linear operators case. The first algorithm implements the Krasnosel'ski-Mann iteration with an inertial effect for which the weak convergence is established under mild assumptions. With the tool of nearly contractive mappings, we introduce a viscosity-type iteration which ensures strong convergence. We apply our results to solve a multiple split monotone variational inclusion problem. A numerical example is given to demonstrate the efficiency of the proposed algorithms.