Iterative solutions of split fixed point and monotone inclusion problems in Hilbert spaces

Our purpose in this paper is to propose an iterative method involving a step-size selected in such a way that its implementation does not require the computation or an estimate of the spectral radius.Using our algorithm, we state and prove a strong convergence theorem of a common solution to a monotone inclusion problem and a fixed point problem of multi-valued Lipschitz hemicontractive-type mappings, whose image under a bounded linear operator is a fixed point of a demicontractive mapping.Our result generalizes some important and recent results in the literature.