Multigraph possibly infinite generalized iterated function systems

In this paper, we introduce the concept of the multigraph possibly infinite generalized iterated function system, which is a generalization, in three directions, of the classical concept of iterated function system due to J. Hutchinson. More precisely: a) it comprises an arbitrary family of contractions allowing to deal with an infinite collection of functions; b) the constitutive contractions of the system are defined on a finite product of metric spaces and take value into a metric space; c) as Mauldin and Williams' concept of graph-directed iterated function system, it is based on the replacement of a single fixed point equation that is satisfied by the attractor with a system of equations. We prove that such a system has a unique attractor and we provide an example.