The development of fractal set theory has been strongly driven by the introduction of new classes of fractal sets, among which the attractors of iterated function systems (IFSs) play a central role. In this work, we study a generalization of the classical IFS framework leading to the construction of fractal interpolation functions (FIFs) in which the standard linear ordinate scaling is replaced by a nonlinear contraction. This modification gives rise to a new family of FIFs associated with contractions of the general integral type, offering a flexible and robust approach for the approximation of experimental and irregular data. Furthermore, we introduce a class of generalized iterated function systems defined by mappings acting on product spaces of the form f:Xm→X, with m∈N*. We prove the existence and uniqueness of the corresponding attractor, thereby extending several classical results from the theory of IFS and fractal interpolation.
Moulahi et al. (Wed,) studied this question.