A singular function with a non-zero finite derivative on a dense set

A singular function with a non-zero finite derivative on a dense set

The authors had exhibited in a previous paper a continuous strictly increasing singular function from [0,1] into [0,1] with a derivative that takes non-zero finite values at the points of an uncountable set. In this article, the construction is improved to encompass a dense set.

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Veröffentlicht in:Nonlinear analysis 2014-01, Vol.95, p.703-713
Hauptverfasser: Fernández Sánchez, Juan, Viader, Pelegrí, Paradís, Jaume, Díaz Carrillo, Manuel
Format: Artikel
Sprache:eng
Schlagworte:
Construction
Derivatives
Mathematical analysis
Nonlinearity
Singular functions
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Beschreibung
Zusammenfassung:The authors had exhibited in a previous paper a continuous strictly increasing singular function from [0,1] into [0,1] with a derivative that takes non-zero finite values at the points of an uncountable set. In this article, the construction is improved to encompass a dense set.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.10.001