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Results tagged with inequalities
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user 94262
for questions involving inequalities, upper and lower bounds.
1
vote
Find the best constant to this bounded inequality
@T.Amdeberhan - I think that the constant $\frac{5}{3}$ is optimal.
Take $x_1=1/4^{m}$, $x_2=1/4^{m-1}$,$\dots$ ,$x_m=1/4$, $x_{m+1}=1$, $x_{m+2}=1/4$, $\dots$, $x_{2m}=1/4^{m-1}$, $x_{2m+1}=1/4^m$, t …
- 343
4
votes
Accepted
Find the best constant to this bounded inequality
These are some thoughts concerning the Question. We have that
\begin{align*}
&S_n(3)=\sum_{1\leq i\leq n}x_i^3< \sum_{i\geq 1}4^{-i}=1/3,\\
&S_n(1,2)=\sum_{1\leq i<j\leq n}x_i x_j^2< \sum_{1\leq i<j}4 …
- 343
8
votes
1
answer
617
views
Inequality for Stirling numbers of the second kind
I stumbled upon the following inequality which, I believe, is true. I was able to prove it for small k, but I have no proof for the general case. Any help is welcome.
Let $n\geq k\geq 1$ then
$$\left …
- 343
2
votes
1
answer
333
views
Given $P\in \mathbb{Z}[x]$ there is a nonzero $Q\in \mathbb{Z}[x]$ such that $H(PQ)\leq M(P)$
I am looking for a proof (or references) for the following result:
If $P\in \mathbb{Z}[x]$ then there exists a nonzero polynomial $Q\in \mathbb{Z}[x]$
such that
$$H(PQ)\leq M(P)$$
where
$H(R)=\max\{| …
- 343