Generalized iterated function systems on the space

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 X I into X, where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.