Note on fractal interpolation function with variable parameters

Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions W-n(x, y) = (a(n)x + e(n), alpha(n)(x)y + psi(n)(x)), n = 1, ... , N. Then, we may define the generalized affine FIF f interpolating a given data set {(x(n), y(n)) is an element of I x R, n = 0, 1, ... , N}, where I = [x(0), x(N)]. In this paper, we discuss the smoothness of the FIF f. We prove, in particular, that f is theta-holder function whenever psi(n) are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.