We consider the Tribin function and its generalization based on the \( {Q}_s^{\ast } \) -representation of real numbers, which is an *s*-symbol encoding of numbers and, generally speaking, a nonself-similar generalization of the *s*-adic representation. By definition, the function *f* associates the number \( x={\varDelta}_{\upalpha_1{\upalpha}_2\dots {\upalpha}_n\dots}^{Q_s^{\ast }}, \) where *α*_{n} ∈ *L* ≡ *A*_{s} × *A*_{s} × … × *A*_{s} × … and *A*_{s} = {0, 1, …, *s* − 1} is an alphabet, *s* ≥ 3; with the number \( y=f(x)={\varDelta}_{\upgamma_1{\upgamma}_2\dots {\upgamma}_n\dots}^{G_2^{\ast }}, \)

where the \( {G}_2^{\ast } \) -representation of numbers has the two-symbol alphabet *A*_{2} = {0, 1}. We prove that the function *f* is well-defined, continuous, and nowhere monotone. Its variational properties are also analyzed.

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Translated from Neliniini Kolyvannya, Vol. 22, No. 3, pp. 380–390, July–September, 2019.

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Prats’ovytyi, M.V., Baranovs’kyi, O.M. & Maslova, Y.P. Generalization of the Tribin Function.
*J Math Sci* **253, **276–288 (2021). https://doi.org/10.1007/s10958-021-05227-3

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