**4. Conclusions and further work**

We reviewed nonlinear fractal interpolation functions by using the Geraghty fixed point theorem instead of the Banach fixed point theorem (or the Rakotch fixed point theorem) since Banach contraction (or Rakotch contraction) is a special case of Geraghty contraction. Theorems 2.1, 2.2 and 2.3 ensure that attractors of constructed nonlinear iterated function systems are graphs of some continuous functions which interpolate the given data. In particular, Examples 1, 2 and 3 show that our results remain still true under essentially weaker conditions on the maps of iterated function systems. The methods presented here can be directly extended to piecewise fractal interpolation functions that are based on recurrent IFS. A premise for future work is to extend these methods to hidden-variable fractal interpolation surfaces as well as to identify the parameters of such surfaces.
