Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 312876, 11 pages
doi:10.1155/2008/312876

Applications of fixed point theorems in the theory of generalized IFS

Abstract

We introduce the notion of a generalized iterated function system (GIFS), which is a finite family of functions fk:Xm → X, where (X,d) is a metric space and m∈ℕ. In case that (X,d) is a compact metric space and the functions fk are contractions, using some fixed point theorems for contractions from Xm to X, we prove the existence of the attractor of such a GIFS and its continuous dependence in the fk's.