Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2018, Volume 14, Number 2, Pages 197–213
DOI: https://doi.org/10.15407/mag14.02.197
(Mi jmag697)
 

This article is cited in 14 scientific papers (total in 14 papers)

Non-differentiable functions defined in terms of classical representations of real numbers

S. O. Serbenyuk

Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereschenkivska St., Kyiv, 01004, Ukraine
References:
Abstract: The present paper is devoted to the functions from a certain subclass of non-differentiable functions. The arguments and values of the considered functions are represented by the $s$-adic representation or the nega-$s$-adic representation of real numbers. The technique of modeling these functions is the simplest as compared with the well-known techniques of modeling non-differentiable functions. In other words, the values of these functions are obtained from the $s$-adic or nega-$s$-adic representation of the argument by a certain change of digits or combinations of digits. Integral, fractal and other properties of the functions are described.
Key words and phrases: nowhere differentiable function, $s$-adic representation, nega-$s$-adic representation, non-monotonic function, Hausdorff–Besicovitch dimension.
Received: 09.05.2017
Revised: 17.07.2017
Document Type: Article
Language: English
Citation: S. O. Serbenyuk, “Non-differentiable functions defined in terms of classical representations of real numbers”, Zh. Mat. Fiz. Anal. Geom., 14:2 (2018), 197–213
Citation in format AMSBIB
\Bibitem{Ser18}
\by S.~O.~Serbenyuk
\paper Non-differentiable functions defined in terms of classical representations of real numbers
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2018
\vol 14
\issue 2
\pages 197--213
\mathnet{http://mi.mathnet.ru/jmag697}
\crossref{https://doi.org/10.15407/mag14.02.197}
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  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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