We construct a continuous nowhere monotone function that depends on infinitely many parameters such that the derivative of this function is equal to zero almost everywhere (in a sense of the Lebesgue measure). It is shown that this function is well-defined and nowhere monotone. Its differential properties are analyzed, the massiveness of the level sets is studied, and the set of maxima and minima of the function and its structural and variational properties are determined.
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Translated from Neliniini Kolyvannya, Vol. 23, No. 4, pp. 502–512, October–December, 2020.
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Pratsiovytyi, M.V., Goncharenko, Y.V., Lysenko, I.M. et al. On One Class of Singular Nowhere Monotone Functions. J Math Sci 263, 268–281 (2022). https://doi.org/10.1007/s10958-022-05925-6
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DOI: https://doi.org/10.1007/s10958-022-05925-6