Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some extensions of Diananda's inequality   Let $M_{n,r}=(\sum_{i=1}^{n}q_ix_i^r)^{\frac {1}{r}}, r \neq 0$ and
$M_{n,0}=\lim_{r \rightarrow 0}M_{n,r}$ be the weighted power means of $n$
non-negative numbers $x_i$ with $q_i > 0$ satisfying $\sum^n_{i=1}q_i=1$. For a
real number $\alpha$ and mutually distinct real numbers $r, s, t$, we define
\begin{align*}
  \Delta_{r,s,t,\alpha}=\Big | \frac
{M^{\alpha}_{n,r}-M^{\alpha}_{n,t}}{M^{\alpha}_{n,r}-M^{\alpha}_{n,s}}\Big |.
\end{align*}
  A result of Diananda gives sharp bounds of $\Delta_{1, 1/2, 0, 1}$ in terms
of functions of $q$ only, where $q=\min q_i$. In this paper, we prove similar
sharp bounds of $\Delta_{r,s,t,\alpha}$ for certain parameters $r, s, t,
\alpha$.

21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga