Geodesic
Continuous functions with complicated local structure defined in terms of alternating Cantor series representation of numbers
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 1, pp. 57-81 
S. O. Serbenyuk. Continuous functions with complicated local structure defined in terms of alternating Cantor series representation of numbers. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 1, pp. 57-81. http://geodesic.mathdoc.fr/item/JMAG_2017_13_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to one infinite parametric class of continuous functions with complicated local structure such that these functions are defined in terms of alternating Cantor series representation of numbers. The main attention is given to differential, integral and other properties of these functions. Conditions of monotony and nonmonotony are found. The functional equations system such that the function from the given class of functions is a solution of the system is indicated.

[1] O.M. Baranovskyi, I.M. Pratsiovyta, M. V. Pratsiovytyi, “On One Function Related to First and Second Ostrogradsky Series”, Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math., 10 (2009), 40–49 (Ukrainian)

[2] M.V. Pratsiovytyi, Fractal Approach to Investigation of Singular Probability Distributions, Dragomanov Nat. Pedagogical Univ. Publ., Kyiv, 1998 (Ukrainian)

[3] M.V. Pratsiovytyi, A. V. Kalashnikov, “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 (Ukrainian) | MR

[4] S.O. Serbenyuk, “On One Nearly Everywhere Continuous and Nowhere Differentiable Function, that Defined by Automaton with Finite Memory”, Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math., 13:2 (2012), 166–182 (Ukrainian) https://www.researchgate.net/publication/292970012

[5] S.O. Serbenyuk, “Representation of Numbers by the Positive Cantor Series: Expansion for Rational Numbers”, Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math., 14 (2013), 253–267 (Ukrainian) https://www.researchgate.net/publication/283909906

[6] S.O. Serbenyuk, “On Some Sets of Real Numbers Such that Defined by Nega-sadic and Cantor Nega-s-adic Representations”, Trans. Natl. Pedagog. Mykhailo Dragomanov Univ. Ser. 1. Phys. Math., 15 (2013), 168–187 (Ukrainian) https://www.researchgate.net/publication/292970280

[7] S.O. Serbenyuk, “Defining by Functional Equations Systems of One Class a Functions, whose Arguments Defined by the Cantor Series”, International Mathematical Conference “Differential Equations, Computational Mathematics, Theory of Functions and Mathematical Methods of Mechanics” dedicated to 100th anniversary of G. M. Polozhy: Abstracts, Kyiv, 2014, 121 (Ukrainian) https://www.researchgate.net/publication/301765329

[8] S.O. Serbenyuk, “Functions, that Defined by Functional Equations Systems in Terms of Cantor Series Representation of Numbers”, Naukovi Zapysky NaUKMA, 165 (2015), 34–40 (Ukrainian) https://www.researchgate.net/publication/292606546

[9] A.F. Turbin, M. V. Pratsiovytyi, Fractal Sets, Functions, Probability Distributions, Naukova dumka, Kyiv, 1992 (Russian) | MR

[10] G. Cantor, “Ueber die Einfachen Zahlensysteme”, Z. Math. Phys., 14 (1869), 121–128 (German)

[11] A. Oppenheim, “Criteria for Irrationality of Certain Classes of Numbers”, Amer. Math. Monthly, 61:4 (1954), 235–241 | DOI | MR | Zbl