关于一类具有分形性质的函数

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI:10.31861/bmj2021.01.23

Y. Goncharenko, M. Pratsiovytyi, S. Dmytrenko, I. Lysenko, S. Ratushniak

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引用次数: 4

摘要

我们考虑了函数的一种推广，它被Bl. Sendov称为“二元自相似函数”。本文分析了研究对象与已知的分形函数类的联系，与数列几何的联系，与双符号$Q_2$-表示的具有独立随机数的随机变量分布的联系，与分形理论的联系。研究了这类函数的结构性质、变分性质、积分性质、微分性质和分形性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ABOUT ONE CLASS OF FUNCTIONS WITH FRACTAL PROPERTIES

We consider one generalization of functions, which are called as «binary self-similar functi- ons» by Bl. Sendov. In this paper, we analyze the connections of the object of study with well known classes of fractal functions, with the geometry of numerical series, with distributions of random variables with independent random digits of the two-symbol $Q_2$-representation, with theory of fractals. Structural, variational, integral, diﬀerential and fractal properties are studied for the functions of this class.

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Bukovinian Mathematical Journal

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