Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument

  • M.V. Pratsovytyi Kyiv Drahomanov Pedagogical University
  • Ya. V. Goncharenko National Pedagogical Dragomanov University, Kyiv, Ukraine
  • I. M. Lysenko National Pedagogical Dragomanov University, Kyiv, Ukraine
  • S.P. Ratushniak Institute of Mathematics, National Academy of Science of Ukraine
Keywords: 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.


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}+
In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.


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How to Cite
Pratsovytyi, M., Goncharenko, Y. V., Lysenko, I. M., & Ratushniak, S. (2021). Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument. Matematychni Studii, 56(2), 133-143.