### References

[1] K.A. Bush, Continuous functions without derivatives, Amer. Math. Monthly 59(1952), No. 4, 222–225. CrossRef

[2] G. Cantor, Ueber die einfachen Zahlensysteme, Z. Math. Phys. 14 (1869), 121–128(German).

[3] G.H. Hardy, Weierstrass’s non-differentiable function, Trans. Amer. Math. Soc. 17(1916), 301–325. CrossRef

[4] J. Hančl, R. Tijdeman, On the irrationality of factorial series, Acta Arith. 118(2005), No. 4, 383–401. CrossRef

[5] J. Gerver, More on the differentiability of the Rieman function, Amer. J. Math. 93(1971), 33–41. CrossRef

[6] H. Minkowski, Zur Geometrie der Zahlen. In: H. Minkowski (ed.) GesammeineAbhandlungen, 2, Druck und Verlag von B.G. Teubner, Leipzig und Berlin, 1911,50–51 (German).

[7] R. Salem, On some singular monotonic functions which are stricly increasing, Trans.Amer. Math. Soc. 53 (1943), 423–439. CrossRef

[8] S. Serbenyuk, On one class of functions with complicated local structure, ŠiauliaiMath. Semin. 11 (19) (2016), 75–88.

[9] S.O. Serbenyuk, Functions defined by functional equations systems in terms of Cantor series representation of numbers, Naukovi Zapysky NaUKMA 165 (2015), 34–40. (Ukrainian). Available from: https://www.researchgate.net/publication/292606546.

[10] S.O. Serbenyuk, Continuous functions with complicated local structure defined interms of alternating Cantor series representation of numbers, Zh. Mat. Fiz. Anal.Geom. 13 (2017), 57–81. CrossRef

[11] Symon Serbenyuk, On one application of infinite systems of functional equations infunction theory, Tatra Mt. Math. Publ. 74 (2019), 117–144. CrossRef

[12] S. Serbenyuk, Nega-Q̃-representation as a generalization of certain alternating representations of real numbers, Bull. Taras Shevchenko Natl. Univ. Kyiv Math. Mech.1 (35) (2016), 32–39. (Ukrainian). Available from: https://www.researchgate.net/publication/308273000.

[13] S. Serbenyuk, Representation of real numbers by the alternating Cantor series,Integers 17 (2017), Paper No. A15.

[14] S. Serbenyuk, On one fractal property of the Minkowski function, Revista de laReal Academia de Ciencias Exactas, Fı́sicas y Naturales. Serie A. Matemáticas 112(2018), No. 2, 555–559. CrossRef

[15] S.O. Serbenyuk, Non-differentiable functions defined in terms of classical representations of real numbers, Zh. Mat. Fiz. Anal. Geom. 14 (2018), 197–213. CrossRef

[16] S. Serbenyuk, One one class of fractal sets, preprint, https://arxiv.org/abs/1703.05262.

[17] S. Serbenyuk, More on one class of fractals, preprint, https://arxiv.org/abs/1706.01546.

[18] S.O. Serbenyuk, One distribution function on the Moran sets, Azerb. J. Math. 10(2020), No. 2, 12–30.

[19] Liu Wen, A nowhere differentiable continuous function constructed using Cantorseries, Math. Mag. 74 (2001), No. 5, 400–402. CrossRef

[20] W. Wunderlich, Eine überall stetige und nirgends differenzierbare Funktion, El.Math. 7 (1952), 73–79 (German).