Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a problem of Janusz Matkowski and Jacek Weso{\l}owski   We study the problem of the existence of increasing and continuous solutions
$\varphi\colon[0,1]\to[0,1]$ such that $\varphi(0)=0$ and $\varphi(1)=1$ of the
functional equation \begin{equation*}
\varphi(x)=\sum_{n=0}^{N}\varphi(f_n(x))-\sum_{n=1}^{N}\varphi(f_n(0)),
\end{equation*} where $N\in\mathbb N$ and $f_0,\ldots,f_N\colon[0,1]\to[0,1]$
are strictly increasing contractions satisfying the following condition
$0=f_0(0)<f_0(1)=f_1(0)<\cdots<f_{N-1}(1)=f_N(0)<f_N(1)=1$. In particular, we
give an answer to the problem posed in the article Remark on BV-solutions of a
functional equation connected with invariant measures by Janusz Matkowski
concerning a very special case of that equation.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int