Hutchinson without Blaschke: An alternative way to fractals

Bessenyei, Mihály and Pénzes, Evelin (2020) Hutchinson without Blaschke: An alternative way to fractals. Expositiones Mathematicae. ISSN 0723-0869 (In Press)

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Abstract

The original approach of Hutchinson to fractals considers the defining equation as a fixed point problem, and then applies the Banach Contraction Principle. To do this, the Blaschke Completeness Theorem is essential. Avoiding Blaschke's result, this note presents an alternative way to fractals via the Kuratowski noncompactness measure. Moreover, our technique extends the existence part of Hutchinson's Theorem to condensing maps instead of contractions.

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