Fractal interpolation surfaces with function vertical scaling factors

By using function vertical scaling factors, a method of construction for the fractal interpolation surfaces on a rectangular domain with arbitrary interpolation nodes is proposed. With the function vertical scaling factors, one class of iterated function systems are constructed. The existence of the unique invariant set of the iterated function system in R 3 is proved. And it is also proved that, for special vertical scaling factors, the invariant set is the graph of a continuous bivariate function passing through the given interpolation nodes.