9 papers
Another look at the Matkowski and Wesołowski problem yielding a new class of solutions
Janusz Morawiec, Thomas Zürcher
The following MW--problem was posed independently by Janusz Matkowski and Jacek Wesołowski in different forms in 1985 and 2009, respectively: Are there increasing and continuous fu…
Monotone mappings and lines
Wiesław Kubiś, Janusz Morawiec, Thomas Zürcher
We study betweenness preserving mappings (we call them \emph{monotone}) defined on subsets of the plane. Once the domain is a convex set, such a mapping is either the restriction o…
On a Problem of Janusz Matkowski and Jacek Wesołowski, II
Janusz Morawiec, Thomas Zürcher
We continue our study started in "On a problem of Janusz Matkowski and Jacek Wesołowski" (see arXiv:1703.08459) of the functional equation \begin{equation*} φ(x)=\sum_{n=0}^{N}φ(f_…
On sets where is finite
Zoltán Buczolich, Bruce Hanson, Martin Rmoutil +1
Given a function , the so-called "little lip" function is defined as follows: \begin{equation*} \operatorname{lip} f(x)=\li…
Space-Filling vs. Luzin's Condition (N)
Thomas Zürcher
Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the f…
Luzin's Condition (N) and Modulus of Continuity
Pekka Koskela, Jan Malý, Thomas Zürcher
In this paper, we establish Luzin's condition (N) for mappings in certain Sobolev-Orlicz spaces with certain moduli of continuity. Further, given a mapping in these Sobolev-Orlicz…