We study structural, integral, differential, variational, and fractal properties of a function f whose argument \( x={\Delta }_{\alpha_1{\alpha}_2\dots {\alpha}_n\dots}^{Q_s^{\ast }} \) is represented by a polybasic s-symbol \( {Q}_s^{\ast } \) -representation (1 < s ∈ N) and its corresponding value is expressed as follows: \( f\left(x={\Delta }_{\alpha_1{\alpha}_2\dots {\alpha}_n\dots}^{Q_s^{\ast }}\right)={a}^{\alpha_1{u}_1+{\alpha}_2{u}_2+\dots +{\alpha}_n{u}_n+\dots }, \) where u1 + u2 + … is a given convergent positive series and αn ∈ {0, 1, …, s - 1}.
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Translated from Neliniini Kolyvannya, Vol. 24, No. 4, pp. 498–517, October–December, 2021.
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Pratsiovytyi, M.V., Vovk, Y.Y., Lysenko, I.M. et al. Superpositions of Functions with Fractal Properties. J Math Sci 273, 248–270 (2023). https://doi.org/10.1007/s10958-023-06497-9
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DOI: https://doi.org/10.1007/s10958-023-06497-9