Box dimension of the graphs of recurrent fractal interpolation functions

Abstract

Abstract Let f be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of f , we define restricted vertical scaling matrices. Then we analyze the irreducibility and monotonicity of spectral radii of these matrices. With these matrices, we study the oscillation sums of f . As a result, we estimate the box dimension of the graph of f by the limits of spectral radii of these matrices. In particular, we obtain an explicit formula of the box dimension of the graph of f under certain constraint conditions.