@article {GwJa2005,
 author="Gertruda Gw\'o\'zd\'z-{\L}ukawska and Jacek Jachymski",
 title={The Hutchinson--Barnsley theory for infinite iterated function systems},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="3",
 pages="441--454",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="19th July, 2005",
 classmath="39B12, 47A35, 47H09, 54H25",
 publisher={AMPAI, Australian Mathematical Society},
 url="http://www.austms.org.au/Publ/Bulletin/V72P3/723-5209-GwJa/index.shtml",
 acknowledgement={We are grateful to Andrzej Komisarski for some useful discussion.},
 abstract={ We show that some results of the Hutchinson--Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if $\{F_i:i\in \N \}$ is a family of Matkowski's contractions on a complete metric space $(X,d)$ such that $(F_ix_0)_{i\in \N }$ is bounded for some $x_0\in X$, then there exists a non-empty bounded and separable set $K$ which is invariant with respect to this family, that is, $K=\bcu \limits _{i\in \N }F_i(K)$. Moreover, given $\si \in \N ^{\N }$ and $x\in X$, the limit $\lim \limits _{n\ra \iy }F_{\si _1}\co F_{\si _n}(x)$ exists and does not depend on $x$. We also study separately the case in which $(X,d)$ is Menger convex or compact. Finally, we answer a question posed by M\'at\'e concerning a finite iterated function system $\{F_1,\ldots ,F_N\}$ with the property that each of $F_i$ has a contractive fixed point. }
}