Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 312876, 11 pages
Research Article

Applications of Fixed Point Theorems in the Theory of Generalized IFS

Alexandru Mihail and Radu Miculescu

Department of Mathematics, Bucharest University, Bucharest, Academiei Street 14, 010014 Bucharest, Romania

Received 9 February 2008; Accepted 22 May 2008

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2008 Alexandru Mihail and Radu Miculescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the notion of a generalized iterated function system (GIFS), which is a finite family of functions fk:XmX, where (X,d) is a metric space and m. 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.