Iterated function systems based on the degree of nondensifiability

Abstract

In the present paper we introduce the concept of iterated function systems (IFS) having at least one ϕ-condensing mapping which belongs to the finite set of self-mappings that define the IFS. It is shown the existence of an invariant for those IFS. Whenever all the self-mappings are ϕ-condensing we prove that the invariant set is compact. We propose some applications of those IFS having ϕ-condensing self-mappings to the superposition operator defined on the Banach space C([0,1]).