Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces

The aim of this work is to propose implicit and explicit viscosity-like methods for finding specific common fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces. Two numerical approaches to solving this problem are considered: an implicit anchor-like algorithm and a nonimplicit one. The considered methods appear to be of practical interests from the numerical point of view and strong convergence results are proved.