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Non-differentiable functions defined in terms of classical representations of real numbers. (English) Zbl 1447.26003
Summary: The present paper is devoted to the functions from a certain subclass of non-differentiable functions. The arguments and values of the considered functions are represented by the \(s\)-adic representation or the nega-\(s\)-adic representation of real numbers. The technique of modeling these functions is the simplest as compared with the well-known techniques of modeling non-differentiable functions. In other words, the values of these functions are obtained from the \(s\)-adic or nega-\(s\)-adic representation of the argument by a certain change of digits or combinations of digits. Integral, fractal and other properties of the functions are described.

26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
11B34 Representation functions
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
39B22 Functional equations for real functions
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