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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… Click to show full 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 ∆. In this way, on the one hand, we generalize a result due to N. Secelean (see The fractal interpolation for countable systems of data, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 14 (2003), 11–19) by considering countable systems consisting of Rakotch contractions rather than Banach contractions. On the other hand, we generalize a result due to S. Ri (see A new idea to construct the fractal interpolation function, Indag. Math., 29 (2018), 962-971) by considering countable (rather than finite) systems consisting of Rakotch contractions. Some exemplifications are provided.
Journal Title: Results in Mathematics
Year Published: 2021
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