References
- [1] ANTONEVICH, A. B.: Linear Functional Equations: Operator Approach.Universitetskoe, Minsk, 1988. (In Russian)
- [2] ACEL, YA.—DOMBR, ZH.: Functional Equations with Several Variables. FIZMATLIT, Moscow, 2003. (In Russian)
- [3] BUSH, K. A.: Continuous functions without derivatives, Amer. Math. Monthly. 59 (1952), 222–225.
- [4] CANTOR, G.:Über die einfachen Zahlensysteme, Zeitschrift Math. Phys. 14 (1869), 121–128. (In German)
- [5] DAUGAVET, I. K.: Aproximate Solution of the Linear Functional Equations. Izd-vo Leningr. un-ta, Leningrad, 1985. (In Russian)
- [6] KALASHNIKOV, A. V.: Some functional correlations, that the singular Salem function holds, Naukovyi Chasopys NPU im. M. P. Dragomanova. Ser. 1. Phizyko-matematychni Nauky [Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math.] 9 (2008), 192–199. (In Ukrainian)
- [7] LIKHTARNIKOV, L. M.: Elementary Introduction to Functional Equations, Lan’, Saint Petersburg, 1997. (In Russian)
- [8] MARSALIA, G.: Random variables with independent binary digits, Ann. Math. Statist. 42 (1971), no. 2, 1922–1929.
- [9] PRATSIOVYTYI, M. V.—KALASHNIKOV, A. V.: On one class of continuous functions with complicated local structure, most of which are singular or nondifferentiable, Trudy Instituta prikladnoi matematiki i mekhaniki NAN Ukrainy, 23 (2011), 178–189. (In Ukrainian)
- [10] PRATS’OVYTYI, M.V. — KALASHNIKOV, A. V.: Self-affine singular and nowhere monotone functions related to the Q-representation of real numbers, Ukrainian Math. J. 65, (2013), no. 3, 448–462. (In Ukrainian)
- [11] PRATSIOVYTYI, M.: Fractal Approach to Investigation of Singular Probability Distributions, Vydavnytstvo NPU im. M. P. Dragomanova, Kyiv, 1998. (In Ukrainian)
- [12] RALKO, YU. V.: Representation of numbers by the Cantor series and some its applications, Naukovyi Chasopys NPU im. M. P. Dragomanova. Ser. 1. Phizyko-matematychni Nauky [Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math.] 10 (2009), 132–140. (In Ukrainian)
- [13] SALEM, R.: On some singular monotonic functions which are stricly increasing,Trans. Amer. Math. Soc. 53 (1943), 423–439.
- [14] SERBENYUK, S. O.: On one nearly everywhere continuous and nowhere differentiable function, that defined by automaton with finite memory, Naukovyi Chasopys NPU im. M. P. Dragomanova. Ser. 1. Phizyko-matematychni Nauky [Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math.] 13 (2012), no. 2, 166–182. (In Ukrainian); https://www.researchgate.net/publication/292970012
- [15] _______ Representation of numbers by the positive Cantor series: expansion for rational numbers, Naukovyi Chasopys NPU im. M. P. Dragomanova. Ser. 1. Phizyko-matematychni Nauky [Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1.Phys. Math.] 14 (2013), 253–267. (In Ukrainian); https://www.researchgate.net/publication/283909906
- [16] _______ On some sets of real numbers such that defined by nega-s-adic and Cantor nega-s-adic representations, Naukovyi Chasopys NPU im. M. P. Dragomanova. Ser. 1. Phizyko-matematychni Nauky [Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math.] 15 (2013), 168–187. (In Ukrainian); https://www.researchgate.net/publication/292970280
- [17] _______ Defining by functional equations systems of one class a functions, whose arguments defined by the Cantor series. In: International Mathematical Conference “Differential Equations, Computational Mathematics, Theory of Functions and Mathematical Methods of Mechanics” dedicated to 100th anniversary of G. M. Polozh ly: Abstracts. Kyiv, 2014. pp. 121. (In Ukrainian); https://www.researchgate.net/publication/301765329
- [18] SERBENYUK, S. O.: Nega-̃Q-representation as a generalization of certain alternating representations of real numbers, Bull. Taras Shevchenko Natl. Univ. Kyiv Math. Mech. 1 (2016), no. 35, 32–39. (In Ukrainian); https://www.researchgate.net/publication/308273000
- [19] _______ Functions, that defined by functional equations systems in terms of Cantor series representation of numbers, Naukovi Zapysky NaUKMA 165 (2015), 34–40. (In Ukrainian); https://www.researchgate.net/publication/292606546
- [20] _______ Continuous functions with complicated local structure defined in terms of alternating Cantor series representation of numbers, Zh. Mat. Fiz. Anal. Geom. 13 (2017), no. 1, 57–81.
- [21] _______ Non-Differentiable functions defined in terms of classical representations of real numbers, Zh. Mat. Fiz. Anal. Geom. 14 (2018), no. 2, 197–213.
- [22] SERBENYUK, S.: On one fractal property of the Minkowski function,Rev.R. Acad. Cienc. Exactas FSPs. Nat. Ser. A, Math. RACSAM 112 (2018), no. 2, 555–559. doi:10.1007/s13398-017-0396-510.1007/s13398-017-0396-5
- [23] SERBENYUK, S. O.: Preserving of Hausdorff-Besicovitch dimension by the monotone singular distribution functions. In: The Second Interuniversity Scientific Conference on Mathematics and Physics for Young Scientists: Abstracts, Kyiv, 2011, pp. 106–107. (In Ukrainian); https://www.researchgate.net/publication/301637057
- [24] _______ On one function, that defined in terms of a nega-̃Q-representation, from a class of functions with complicated local structure. In: The Fourth All-Ukrainian Scientific Conference of Young Scientists on Mathematics and Physics: Abstracts. Kyiv, 2015, pp. 52. (In Ukrainian); https://www.researchgate.net/publication/301765100
- [25] _______ On two functions with complicated local structure. In :The Fifth International Conference on Analytic Number Theory and Spatial Tessellations: Abstracts, Kyiv: Institute of Mathematics of the National Academy of Sciences of Ukraine and Institute of Physics and Mathematics of the National Pedagogical Dragomanov University, 2013, pp. 51–52. https://www.researchgate.net/publication/
- [26] _______ On one class of functions with complicated local structure,Šiauliai Math. Semin. 11 (2016), no. 19, 75–88.
- [27] _______ Representation of real numbers by the alternating Cantor series, Integers 17 (2017), no. A15, pp. 27.
- [28] SERBENYUK, S. O.: Nega-̃Q-representation of real numbers. In: International Conference “Probability, Reliability and Stochastic Optimization”: Abstracts, Kyiv, Taras Shevchenko National University of Kyiv, 2015, pp. 24. https://www.researchgate.net/publication/
- [29] _______ On one nearly everywhere continuous and nowhere differentiable function, that defined by automaton with finite memory. In: International Scientific Conference “Asymptotic Methods in the Differential Equations Theory”: Abstracts, Kyiv, 2012, pp. 93. (In Ukrainian); https://www.researchgate.net/publication/301765319
- [30] TURBIN, A.—PRATSIOVYTYI, M.: Fractal Sets, Functions, Probability Distributions, Naukova Dumka, Kyiv, 1992. (In Russian)
- [31] ZAMFIRESCU, T.: Most monotone functions are singular,Amer. Math. Mon. 88 (1981), 47–49.