Based on a result of de Rham, we give a family of functions solving the Matkowski and Wesołowski problem. This family consists of Hölder continuous functions, and it coincides with the whole family of solutions to the Matkowski and Wesołowski problem found earlier by a different method. Moreover, applying some results due to Hata and Yamaguti and due to Berg and Krüppel, we prove that there are functions solving the Matkowski and Wesołowski problem that are not Hölder continuous.

中文翻译：

---

解决Matkowski和Wesołowski问题的新方法的新方法

基于de Rham的结果，我们给出了一系列解决Matkowski和Wesołowski问题的函数。该族由Hölder连续函数组成，它与通过不同方法先前发现的Matkowski和Wesołowski问题的整个解决方案族一致。此外，根据Hata和Yamaguti以及Berg和Krüppel的结果，我们证明存在一些解决Matkowski和Wesołowski问题的函数，这些函数不是Hölder连续的。