Fractal interpolation functions with variable parameters and their analytical properties

Based on a widely used class of iterated function systems (IFSs), a class of IFSs with variable parameters is introduced, which generates the fractal interpolation functions (FIFs) with more flexibility. Some analytical properties of these FIFs are investigated in the present paper. Their smoothness is first considered and the related results are presented in three different cases. The stability is then studied in the case of the interpolation points having small perturbations. Finally, the sensitivity analysis is carried out by providing an upper estimate of the errors caused by the slight perturbations of the IFSs generating these FIFs.