More on one class of fractals

This article is devoted to Cantor-like sets. We describe topological, metric and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own representations. Also, such properties are considered for the cases of special type of sets, i.e., sets whose elements represented in terms of certain series related with classical representations of real numbers.Comment: 14 page

Certain singular distributions and fractals

In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of certain self-similar fractals under the action of some singular distributions, are investigated.Comment: 22 pages. This research is an extension of investigation arXiv:1808.00395. arXiv admin note: text overlap with arXiv:1706.0154

Non-differentiable functions defined in terms of classical representations of real numbers

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 representation or the nega-s-adic representation of real numbers. The technique of modeling such functions is the simplest as compared with well-known techniques of modeling non-differentiable functions. In other words, 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.Comment: 16 page