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Журн. матем. физ., анал., геом., 2018, том 14, номер 2, страницы 197–213
(Mi jmag697)
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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
Аннотация:
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.
Ключевые слова и фразы:
nowhere differentiable function, $s$-adic representation, nega-$s$-adic representation, non-monotonic function, Hausdorff–Besicovitch dimension.
DOI:
https://doi.org/10.15407/mag14.02.197
Полный текст:
PDF файл (388 kB)
Список литературы:
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Тип публикации:
Статья
MSC: 26A27, 11B34, 11K55, 39B22 Поступила в редакцию: 09.05.2017 Исправленный вариант: 17.07.2017
Язык публикации: английский
Образец цитирования:
S. O. Serbenyuk, “Non-differentiable functions defined in terms of classical representations of real numbers”, Журн. матем. физ., анал., геом., 14:2 (2018), 197–213
Цитирование в формате AMSBIB
\RBibitem{Ser18}
\by S.~O.~Serbenyuk
\paper Non-differentiable functions defined in terms of classical representations of real numbers
\jour Журн. матем. физ., анал., геом.
\yr 2018
\vol 14
\issue 2
\pages 197--213
\mathnet{http://mi.mathnet.ru/jmag697}
\crossref{https://doi.org/10.15407/mag14.02.197}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/jmag697 http://mi.mathnet.ru/rus/jmag/v14/i2/p197
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
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