Generalized IFSs on noncompact spaces
This paper extends earlier work by the authors [Fixed Point Theory Appl. 2008, Article ID 312876 (2008; Zbl 1201.54037)] concerning iterated function schemes on compact metric spaces. Here the case of a finite family of Lipschitz contractions \(f_1,\dots,f_n:X^m\to X\) on a complete metric space is studied. The existence of an attractor is shown, and the Hausdorff-Pompeiu distance between such attractors is found, showing continuity in the functions. Examples are given to show that this is a natural extension of the notion of iterated function scheme on compact metric spaces.
scientific article; zbMATH DE number 5692340