RUS  ENG
Full version
JOURNALS // Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry] // Archive

Zh. Mat. Fiz. Anal. Geom., 2018 Volume 14, Number 2, Pages 197–213 (Mi jmag697)

This article is cited 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.

MSC: 26A27, 11B34, 11K55, 39B22

Received: 09.05.2017
Revised: 17.07.2017

Language: English

DOI: 10.15407/mag14.02.197



© Steklov Math. Inst. of RAS, 2024