Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 2, pp. 197-213   https://doi.org/10.15407/mag14.02.197     ( to contents , go back )
https://doi.org/10.15407/mag14.02.197

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
E-mail: simon6@ukr.net

Received May 9, 2017, revised June 17, 2017.

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.

Mathematics Subject Classification 2010: 26A27, 11B34, 11K55, 39B22.
Key words: nowhere differentiable function, s-adic representation, nega-s-adic representation, non-monotonic function, Hausdorff–Besicovitch dimension.

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