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arXiv · 1602.01513

Continuous functions with complicated local structure that defined in terms of alternating Cantor series representation of numbers

Symon Serbenyuk
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Abstract

The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by the alternating Cantor series are investigated. The functional equations systems, that investigating functions are unique solution of these systems in the class of determined and bounded on $[0;1]$ functions are indicated. The investigation was represented in seminar on fractal analysis of Institute of Mathematics of the National Academy of Sciences of Ukraine on, October 16, 2014 (http://www.imath.kiev.ua/events/index.php?seminarId=21&archiv=1). The following investigations in the list of references in the article one can to find by the corresponding links: [6] (http://fmi.npu.edu.ua/images/files/publications/naukchasopys1/NZ2013_15.pdf ) [7] (http://fmi.npu.edu.ua/images/files/publications/naukchasopys1/NZ2013_14.pdf) [8] (http://fmi.npu.edu.ua/images/files/publications/naukchasopys1/NZ2012_13_2.pdf) [9](http://www.ekmair.ukma.edu.ua/bitstream/handle/123456789/7409/Serbeniuk_Funktsii_oznacheni_systemamy.pdf)

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BibTeXRIS

Symon Serbenyuk. 2016-02-04. Continuous functions with complicated local structure that defined in terms of alternating Cantor series representation of numbers. https://arxiv.org/abs/1602.01513

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