Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the $p$-angular distance and characterizations of inner
  product spaces   Based on a suitable improvement of a triangle inequality, we derive new
mutual bounds for $p$-angular distance $\alpha_p[x,y]=\big\Vert \Vert
x\Vert^{p-1}x- \Vert y\Vert^{p-1}y\big\Vert$, in a normed linear space $X$. We
show that our estimates are more accurate than the previously known upper
bounds established by Dragomir, Hile and Maligranda. Next, we give several
characterizations of inner product spaces with regard to the $p$-angular
distance. In particular, we prove that if $|p|\geq |q|$, $p\neq q$, then $X$ is
an inner product space if and only if for every $x,y\in X\setminus \{0\}$,
$${\alpha_p[x,y]}\geq \frac{{\|x\|^{p}+\|y\|^{p} }}{\|x\|^{q}+\|y\|^{q}
}\alpha_q[x,y].$$

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci