This paper presents a method to construct nonlinear hidden variable fractal interpolation functions (FIFs) and their stability results. We ensure that the projections of attractors of vector-valued nonlinear iterated function systems (IFSs) constructed by Rakotch contractions and function vertical scaling factors are graphs of some continuous functions interpolating the given data. We also give an explicit example illustrating obtained results. Then, we get the stability results of the constructed FIFs in the case of the generalized interpolation data having small perturbations.

In this paper, we present the construction of new nonlinear recurrent hidden variable fractal interpolation surfaces (RHVFISs) with function vertical scaling factors. We use Rakotch’s fixed point theorem which is a generalization of Banach’s fixed point theorem to get new nonlinear fractal surfaces. We construct recurrent vector-valued iterated function systems (IFSs) with function vertical scaling factors on rectangular grids and generate flexible and diverse RHVFISs which are attractors of the IFSs. We also give an explicit example to show the effectiveness of obtained results.