Generalized iterated function systems on the space l∞(X)

In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space Xi into X, where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given. (C) 2013 Elsevier Inc. All rights reserved.