On generalized iterated function systems defined on ℓ∞-sum of a metric space

On the existence of the Hutchinson measure for generalized iterated function systems

“…As was remarked, the class of GIFSs' attractors is essentially wider than the class of IFSs' attractors. In fact, there are sets (even subsets of the real line) which are attractors of GIFSs of order 2 consisting of generalized Banach contractions, and which are not homeomorphic to the attractor of IFS consisting of Matkowski contractions-see [9].…”

“…In recent papers [9,21], the theory of GIFSs was extended to "infinite order", that is, to maps defined on spaces of bounded sequences of elements of a given space X . In particular, in [9] we defined and studied the code space for such kind of GIFSs and proved counterparts of Theorems 2.4 and 2.9. Hence the question arises: Problem 5.6 Can Theorem 4.3 be extended to GIFSs of infinite order?…”

A fixed point theorem for mappings on the l∞-sum of a metric space and its application

“…As we have already mentioned, Secelean [8] used his theorem to study the Hutchinson-Barnsley theory of fractals for maps defined on ℓ ∞ (X). In our paper [5] we use results of this article to obtain an appropriate version of the Hutchinson-Barnsley theory in such setting.…”

Iterated Functions Systems Composed of Generalized θ-Contractions

“…The framework of IFS theory has been extended to generalized contractions, countable IFSs, multifunction systems and more general spaces by many authors in the last two decades, see for instance [13][14][15][16][17][18][19]. In particular, Mihail and Miculescu [20,21] considered mappings from a finite Cartesian product X × • • • × X into X instead of self-mappings of a metric space X. Dumitru [22] enhanced the work of Miculescu and Mihail by taking a generalized IFS composed of Meir-Keeler type mappings.…”