Nonlinear Fractal Interpolation Functions Induced by General Integral Contractions

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.