Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Applications of Fixed Point Theorems in the Theory of Generalized IFS | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 312876 11 pages doi 2008 312876 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 Correspondence should be addressed to Radu Miculescu miculesc@ Received 9 February 2008 Accepted 22 May 2008 Recommended by Hichem Ben-El-Mechaiekh 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 e 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. Copyright 2008 A. Mihail and R. 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. 1. Introduction We start with a short presentation of the notion of an iterated function system IFS one of the most common and most general ways to generate fractals. This will serve as a framework for our generalization of an iterated function system. Then we introduce the notion of a GIFS which is a finite family of functions fk Xm X where X d is a metric space and m e 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. IFSs were introduced in their present form by Hutchinson see 1 and popularized by Barnsley see 2 . In the last period IFSs have attracted much attention being used from researchers who work on autoregressive time .
