Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fixed point theorem for mappings on the $\ell_\infty$-sum of a metric
  space and its application   The aim of this paper is to prove a counterpart of the Banach fixed point
principle for mappings $f: \ell_\infty(X) \to X$, where $X$ is a metric space
and $\ell_\infty(X)$ is the space of all bounded sequences of elements
from~$X$. Our result generalizes the theorem obtained by Miculescu and Mihail
in 2008, who proved a~counterpart of the Banach principle for mappings
$f:X^m\to X$, where $X^m$ is the Cartesian product of $m$ copies of $X$. We
also compare our result with a recent one due to Secelean, who obtained a
weaker assertion under less restrictive assumptions. We illustrate our result
with several examples and give an application.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol