Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument
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...
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Ivan Franko National University of Lviv
2021-12-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/275 |
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| author | M.V. Pratsovytyi Ya. V. Goncharenko I. M. Lysenko S.P. Ratushniak |
| author_facet | M.V. Pratsovytyi Ya. V. Goncharenko I. M. Lysenko S.P. Ratushniak |
| author_sort | M.V. Pratsovytyi |
| collection | DOAJ |
| description | 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 $f$. |
| format | Article |
| id | doaj-art-6b2093afbf06480eb809b8a93727fa8c |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2021-12-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-6b2093afbf06480eb809b8a93727fa8c2025-08-20T03:33:11ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202021-12-0156213314310.30970/ms.56.2.133-143275Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argumentM.V. Pratsovytyi0Ya. V. Goncharenko1I. M. Lysenko2S.P. Ratushniak3Kyiv Drahomanov Pedagogical UniversityNational Pedagogical Dragomanov University, Kyiv, UkraineNational Pedagogical Dragomanov University, Kyiv, UkraineInstitute of Mathematics, National Academy of Science of UkraineWe 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 $f$.http://matstud.org.ua/ojs/index.php/matstud/article/view/275two-symbol q2 -representation of numbers of unit segment; function with fractal properties; si- ngular function; hausdorff-besicovith dimension; a set of incomplete sums of row. |
| spellingShingle | M.V. Pratsovytyi Ya. V. Goncharenko I. M. Lysenko S.P. Ratushniak Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument Математичні Студії two-symbol q2 -representation of numbers of unit segment; function with fractal properties; si- ngular function; hausdorff-besicovith dimension; a set of incomplete sums of row. |
| title | Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument |
| title_full | Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument |
| title_fullStr | Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument |
| title_full_unstemmed | Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument |
| title_short | Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument |
| title_sort | fractal functions of exponential type that is generated by the mathbf q 2 representation of argument |
| topic | two-symbol q2 -representation of numbers of unit segment; function with fractal properties; si- ngular function; hausdorff-besicovith dimension; a set of incomplete sums of row. |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/275 |
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