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Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument
Author(s) -
M. V. Prats’ovytyĭ,
Ya. V. Goncharenko,
Iryna Lysenko,
S. P. Ratushniak
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.56.2.133-143
Subject(s) - combinatorics , alpha (finance) , mathematics , type (biology) , function (biology) , exponential function , physics , mathematical analysis , statistics , ecology , construct validity , evolutionary biology , biology , psychometrics
We consider function $f$ which is depended on the parameters $0<a\in R$, $q_{0n}\in (0;1)$, $n\in N$ and convergent positive series $v_1+v_2+...+v_n+...$, defined by equality $f(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=a^{\varphi(x)}$, where $\alpha_n\in \{0,1\}$, $\varphi(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\alpha_1v_1+...+\alpha_nv_n+...$, $q_{1n}=1-q_{0n}$, $\Delta^{Q_2^*}_{\alpha_1...\alpha_n...}=\alpha_1q_{1-\alpha_1,1}+\sum\limits_{n=2}^{\infty}\big(\alpha_nq_{1-\alpha_n,n}\prod\limits_{i=1}^{n-1}q_{\alpha_i,i}\big)$.In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.

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