A very general framework for fractal interpolation functions

M. Barnsley introduced the concept of fractal interpolation function as an alternative method for construction of interpolation functions. Such a function is the attractor of an iterated function system comprising Banach contractions (on the product of two real compact intervals) with respect to the second variable. In the present paper we enlarge classical Barnsley's framework by allowing the constitutive functions of the system to be Edelstein contractions in the second variable. As the class of Edelstein contractions contains the class of Matkowski contractions, the class of Meir-Keeler contractions, the class of F -contractions and the class of theta contractions, we provide a much more flexible framework for the construction of fractal interpolation functions. We also obtain a result concerning the estimation of lower and upper box dimensions of the graph of a fractal interpolation function constructed via our general method. (c) 2024 Elsevier Inc. All rights reserved.