  We associate to each iterated function system consisting of
phi-max-contractions an operator (on the space of continuous functions from the
shift space on the metric space corresponding to the system) having a unique
fixed point whose image turns out to be the attractor of the system. Moreover,
we prove that the unique fixed point of the operator associated to an iterated
function system consisting of convex contractions is the canonical projection
from the shift space on the attractor of the system.
