21 citations · 200 across the 33 of their papers we have counts for
7 papers · 1 filter
Cantor series expansions of rational numbers
Symon Serbenyuk
This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the…
More on one class of fractals
Symon Serbenyuk
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restricti…
Non-differentiable functions defined in terms of classical representations of real numbers
Symon Serbenyuk
The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic repr…
On one class of fractal sets
Symon Serbenyuk
In the present article a new class of all sets represented in the following form is introduced: $$ \mathbb S_{(s,u)}\equiv\left\{x: x= Δ^{s}_{{\underbrace{u...u}_{α_1-1}} α_1{\…
On one nearly everywhere continuous and nowhere differentiable function, that defined by automaton with finite memory
Symon Serbenyuk
This paper is devoted to the investigation of the following function where $φ(i…
Cantor series and rational numbers
Symon Serbenyuk
The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by…
On one fractal property of the Minkowski function
Symon Serbenyuk
It is shown in the present article that the Minkowski function does not preserve the Hausdorff-Besicovitch dimension. Results of this article were presented by the author of this a…