Open Access

Applications of Fixed Point Theorems in the Theory of Generalized IFS

Fixed Point Theory and Applications20082008:312876

DOI: 10.1155/2008/312876

Received: 9 February 2008

Accepted: 22 May 2008

Published: 27 May 2008

Abstract

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

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Authors’ Affiliations

(1)
Department of Mathematics, Bucharest University

Copyright

© A. Mihail and R. Miculescu. 2008

This article is published under license to BioMed Central Ltd. 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.