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Les schémas de subdivision de Besicovitch et de Cantor

Les schémas de subdivision de Besicovitch et de Cantor We introduce the Besicovitch and Cantor subdivision schemes with various examples. We identify two Besicovitch schemes whose limit fonctions are the Besicovitch function B and the Singh function S. It is recognized that both functions have at any point neither a right derivative, nor a left derivative, finite or infinite. We discover that B at point 4/7 has an infinite right derivative contrary to what is recognized. Nonetheless, we confirm that S has no one-sided derivatives, neither finite nor infinite. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales mathématiques du Québec Springer Journals

Les schémas de subdivision de Besicovitch et de Cantor

Dubuc, Serge
Annales mathématiques du Québec , Volume 44 (2) – Oct 18, 2020
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Publisher
Springer Journals
Copyright
Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2020
ISSN
2195-4755
eISSN
2195-4763
DOI
10.1007/s40316-020-00131-9
Publisher site
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Abstract

We introduce the Besicovitch and Cantor subdivision schemes with various examples. We identify two Besicovitch schemes whose limit fonctions are the Besicovitch function B and the Singh function S. It is recognized that both functions have at any point neither a right derivative, nor a left derivative, finite or infinite. We discover that B at point 4/7 has an infinite right derivative contrary to what is recognized. Nonetheless, we confirm that S has no one-sided derivatives, neither finite nor infinite.

Journal

Annales mathématiques du Québec – Springer Journals

Published: Oct 18, 2020

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