Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a nonlinear $p$-inequality   We obtain the necessary and sufficient conditions on real sequences
$(\beta_{i})$ for the satisfaction of the generalized triangle inequality
\begin{equation} \|\sum_{i\geq 1} v_{i}\|^{p} \leq \sum_{i\geq 1}{{\beta_{i}}
\| v_{i}\|^{p}}.\tag{I} \end{equation} Sequences $(\beta_{i})$ for which the
reverse of the inequality (I) holds are characterized as well.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas