A countable fractal interpolation scheme involving Rakotch contractions

TL;DR

This paper proves that for any countable set of data points, one can construct a countable iterated function system with Rakotch contractions whose attractor is a fractal interpolation function passing through those points.

Contribution

It introduces a novel countable fractal interpolation scheme using Rakotch contractions, expanding the class of functions that can be generated from countable data sets.

Findings

Existence of a countable IFS with Rakotch contractions for given data

Attractor of the IFS is the fractal interpolation function

Applicable to countable data systems

Abstract

The main result of this paper states that for a given countable system of data, there exists a countable iterated function system consisting of Rakotch contractions, such that its attractor is the graph of a fractal interpolation function corresponding to the given countable system of data.