Shape preserving rational cubic fractal interpolation function

A new type of C1 Fractal Interpolation Function (FIF) is developed using the Iterated Function System (IFS) which contains the rational spline. The numerator of this rational spline contains cubic polynomial and the denominator of the rational spline contains quadratic polynomial. We find uniform error bound between the original function which belongs to the class C2 and the FIF. We described suitable conditions on scaling factors and shape parameters such that they preserve the shape properties which are inherited in the data.