García Macías, Gonzalo, Mora, Gaspar
Iterated function systems based on the degree of nondensifiability
Journal of Fractal Geometry. 2022, 9(3-4): 357-372. https://doi.org/10.4171/jfg/121
URI: http://hdl.handle.net/10045/135738
DOI: 10.4171/jfg/121
ISSN: 2308-1309 (Print)
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]).
Keywords:Fixed points, Degree of nondensifiability, Iterated function system, Invariant sets, Fractals, Invariance operator, α-dense curves
EMS Press
info:eu-repo/semantics/article