  Assuming that the absence of perturbations guarantees weak or strong
convergence to a common fixed point, we study the behavior of perturbed
products of an infinite family of nonexpansive operators. Our main result
indicates that the convergence rate of unperturbed products is essentially
preserved in the presence of perturbations. This, in particular, applies to the
linear convergence rate of dynamic string averaging projection methods, which
we establish here as well. Moreover, we show how this result can be applied to
the superiorization methodology.
