A method for specifying functions defined in terms of the Q3 - representation of real numbers and invariants in their representation.

I. V. Zamrii

Abstract


---

Keywords


Q3 -representation of real numbers; continuous function; lump-singular function; equivalent to the definition (method of assignment); set of function level; system of equations

References


Pratsiovytyi M. V. (1998). Fractal Approach in Studies of Singular Distributions. Kyiv: View of the NPU named after M. P. Dragomanov (in ukrainian).

Turbin A. F., Pratsiovytyi M. V. (1992). Fractal sets, functions, distributions. K.:Naukova dumka (in russian).

Albeverio S., Baranovskyi O., Kondratiev Yu., Pratsiovytyi M. (2013). On one class of functions related to Ostrogradsky series and containing singular and nowhere monotonic functions. Scientific journal NPU of N. P. Drahomanov. Series 1. Physics and mathematics, No 15, 35-55.

Billingsley P. (1983). The singular function on bold play. Am. Sci., 71., 392-397.

Peter R. Massopust. (1995). Fractal functions, fractal surfaces, and wavelets. Academic Press; 1 edition, 383.

Pratsiovytyi M. V., Kalashnikov A. V. (2013). Self-infinitive singular and nowhere monotonic functions associated with the image of real numbers. Ukr. Mate. Journ, 65(3), 405-417 (in ukrainian).

Pratsiovytyi M., Vasylenko N. (2013). Fractal properties of functions defined in terms of Q -representation. Int. Journal of Math. Analysis, 7(64), 3155-3169.

Zamrii I. V., Pratsiovytyi M. V. (2015). Signularity of invertor the digitizer Q3-representation of the fractional part of the real number, its fractal and integral. Nonlinear oscillations (ISSN 1562-3076), 18(1), 55-70 (in ukrainian).

Pratsiovytyi M. V., Zamrii I. V. (2015). Continuous functions preserving digit 1 in the Q3-representation of number. Bukovinsky Mathematical Journal, 3(3-4), 142-159 (in ukrainian).

Salem R. (1943). On some singular monotonic function which are strictly increasing. Trans. Amer. Math. Soc, 53(3), 427-439.

Osaulenko R. Yu. (2016). A group of continuous transformations of a segment that preserves the frequency of digits -the image of a number. Collected Works of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 13(3), 191-204 (in ukrainian).


Full Text: PDF (Українська)
Archive
2013 16
2014 16
2015 16
2016 1
2017 1
2018 1
2019

1

User

Language

Journal Content

Browse