Inertial iterative algorithm with self-adptive step sizes for split null point problems and common fixed point problems

In this paper, we introduce a self-adaptive inertial iterative algorithm for solving a split null point problem with maximal monotone operators and a common fixed point problem of a finite family of multivaluted demicontractive mappings and an infinite family of strict pseudo-contractive mappings between a Banach space and a Hilbert space.Next, we prove a strong convergence result for the proposed algorithm under some mild conditions on the control parameters without a priori estimate of the norm of the linear operator involved.Then, we give a numerical example to illustrate the effectiveness of the algorithm.