A note on fractal dimension for a class of fractal interpolation functions

Abstract

The fractal interpolation functions with appropriate iterated function systems (IFSs) provide a method to perturb and approximate a continuous function on a compact interval I. This method produces a class of functions f α ∈ C(I), where α is a scale parameter. As essential parameters of the IFS, the scaling factors have important consequences in the properties of the function f α. Also, the interpolant or a certain derivative of it may have a non-integer box-counting dimension depending on the scaling factors magnitude. In this talk, we discuss an exact estimation of box dimension of α-fractal functions under suitable hypotheses on IFSs.