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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
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
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
Linking options:
https://www.mathnet.ru/eng/jmag697 https://www.mathnet.ru/eng/jmag/v14/i2/p197
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Abstract page: | 163 | Full-text PDF : | 38 | References: | 21 |
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