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A Countable Fractal Interpolation Scheme Involving Rakotch Contractions

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Abstract

The main result of this paper states that for a given countable system of data \(\varDelta \), 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 \(\varDelta \). In this way, on the one hand, we generalize a result due to Secelean (see Univ Beograd Publ Elektrotehn Fak Ser Mat 14:11–19, 2003) by considering countable systems consisting of Rakotch contractions rather than Banach contractions. On the other hand, we generalize a result due to Ri (see Indag Math 29:962–971, 2018) by considering countable (rather than finite) systems consisting of Rakotch contractions. Some exemplifications are provided.

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  1. Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Bulevardul Eroilor 29, Brasov, Romania

    Cristina Maria Pacurar

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  1. Cristina Maria Pacurar
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Pacurar, C.M. A Countable Fractal Interpolation Scheme Involving Rakotch Contractions. Results Math 76, 161 (2021). https://doi.org/10.1007/s00025-021-01470-x

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