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.
Поступила в редакцию: 09.05.2017 Исправленный вариант: 17.07.2017
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
\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:
https://www.mathnet.ru/rus/jmag697
https://www.mathnet.ru/rus/jmag/v14/i2/p197
Эта публикация цитируется в следующих 14 статьяx:
Symon Serbenyuk, “The generalized Salem functions defined in terms of certain Cantor expansions”, J Anal, 2024
S. Serbenyuk, “Singular Modifications Of A Classical Function”, Acta Math. Hungar., 172:1 (2024), 206
Symon Serbenyuk, “Relationships between singular expansions of real numbers”, J Anal, 2024
Symon Serbenyuk, “Functional equations, alternating expansions, and generalizations of the Salem functions”, Aequat. Math., 2023
Symon Serbenyuk, “A certain modification of classical singular function”, Bol. Soc. Mat. Mex., 29:3 (2023)
Symon Serbenyuk, “Some types of numeral systems and their modeling”, J Anal, 31:1 (2023), 149
Symon Serbenyuk, “Some Fractal Properties of Sets Having the Moran Structure”, Tatra Mountains Mathematical Publications, 81:1 (2022), 1
Serbenyuk Symon, “Certain Singular Distributions and Fractals”, Tatra Mountains Mathematical Publications, 79:2 (2022), 163
S. Serbenyuk, “Systems of functional equations and generalizations of certain functions”, Aequ. Math., 95:5 (2021), 801–820
Symon Serbenyuk, “Certain functions defined in terms of Cantor series”, Журн. матем. физ., анал., геом., 16:2 (2020), 174–189
S. O. Serbenyuk, “One distribution function on the moran sets”, Azerbaijan J. Math., 10:2 (2020), 12–30
Symon Serbenyuk, “Generalizations of Certain Representations of Real Numbers”, Tatra Mountains Mathematical Publications, 77:1 (2020), 59
Symon Serbenyuk, “On certain maps defined by infinite sums”, J Anal, 28:4 (2020), 987
Symon Serbenyuk, “On One Application of Infinite Systems of Functional Equations in Function Theory”, Tatra Mountains Mathematical Publications, 74:1 (2019), 117
Цитирование в формате AMSBIB
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