Oleksandr V. Maslyuchenko

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20242026

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math.FA2026

Operators arising from invariant measures under some class of multidimensional transformations

Oleksandr V. Maslyuchenko, Janusz Morawiec, Thomas Zürcher

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examini…

math.FA2025

Classification of Lipschitz derivatives in terms of semicontinuity and the Baire limit functions

Oleksandr V. Maslyuchenko, Ziemowit M. Wójcicki

We introduce the generalized notion of semicontinuity of a function defined on a topological space and derive the useful classification of the so-called Lipschitz derivatives of fu…

math.FA2025

Centered Takagi--van der Waerden functions and their Lipschitz derivatives

Oleksandr V. Maslyuchenko, Ziemowit M. Wójcicki

Using a modification of a generalized Takagi-van der Waerden function on a metric space we prove that for any closed subset of a metric space without isolated points there exists a…

math.FA2024

Takagi-van der Waerden functions in metric spaces and its Lipschitz derivatives

Oleksandr Maslyuchenko, Ziemowit Wójcicki

We introduce the Takagi--van der Waerden function with parameters $a > b > 0$ by setting $f_{a, b} (x) = n = 1 \sum \infty b^{n} d (x, S_{n})$ , where $S_{n}$ is a maximal $\frac…