Iterated function systems based on the degree of nondensifiability (Q6172325)

Summary: In the present paper we introduce the concept of iterated function systems (IFS) having at least one \(\phi \)-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 \(\phi\)-condensing we prove that the invariant set is compact. We propose some applications of those IFS having \(\phi\)-condensing self-mappings to the superposition operator defined on the Banach space \(\mathcal{C} ( [ 0 , 1 ] )\).