The Hutchinson–barnsley Theory for Infinite Iterated Function Systems


We show that some results of the Hutchinson–Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if {Fi : i ∈ N} is a family of Matkowski’s contractions on a complete metric space (X, d) such that (Fix0)i∈N is bounded for some x0 ∈ X, then there exists a non-empty bounded and separable set K which is… (More)