Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 1, pp. 57-81   https://doi.org/10.15407/mag13.01.057     ( to contents , go back )
https://doi.org/10.15407/mag13.01.057

Continuous Functions with Complicated Local Structure Defined in Terms of Alternating Cantor Series Representation of Numbers

S.O. Serbenyuk

Institute of Mathematics of the National Academy of Sciences of Ukraine 3 Tereschenkivska Str., Kyiv-4 01004, Ukraine
E-mail: simon.mathscience@imath.kiev.ua, simon6@ukr.net

Received October 22, 2015, revised May 18, 2016

Abstract

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.

Mathematics Subject Classification 2000: 39B72, 26A27, 26A30, 11B34, 11K55.
Key words: alternating Cantor series, functional equations system, monotonic function, continuous nowhere monotonic function, singular function, nowhere differentiable function, distribution function.

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