Tagged Questions

321 views

Does this simple inequality have a name?

Let $x_{1},\ldots,x_{n}$ be nonnegative numbers such that $m \leq x_{i} \leq M$. Let $$S=\sum_{i=1}^{n}{x_{i}}$$ and $$Q=\sum_{i=1}^{n}{x_{i}^{2}}.$$ Then $$Q \leq S(M+m)-nMm.$$ This has ...
108 views

Concentration inequalities in $\ell_{\infty}$ for sums of iid random (“nice”) functions?

I'm looking for "tail-bound-like" inequalities that look like this (I state a specific setting but more general settings are interesting): Let $D$ be a distribution on a set of "nice" functions ...
163 views

An inequality involving Bessel functions of imaginary order

The following inequality: $$\frac{\pi k}{\sinh{(\pi k)}}\;|J_{ik}(\tau)|^2\le 1,\;\;\;k,\tau\ge 0,$$ for Bessel function $J_{ik}(\tau)$, I found in http://link.springer.com/article/10.1134%2F1.558677 ...
261 views

247 views

how to proof this Stirling related equation

here is what I need to proof, have no idea were to start. I know there is some connection with the Stirling theorem. $$\sum_{i=0}^{d}\binom{m}{i} \leq \left ( \frac{em}{d} \right )^{d}$$ I tried ...
242 views

Inequalities Involving Wedge Product (Reference Request)

Hello, I'm looking for references on various inequalities involving the wedge product and exterior forms. The only references I could hunt down are references on Hadamard-Schwarz Inequality. The ...
521 views

The Farkas Lemma says that if a system of linear inequalities implies yet another linear inequality, then this last inequality can be obtained by taking a positive linear combination of the ...
423 views

Shapiro inequality for $n=23$

Is the Shapiro inequality for $n=23$ an open problem? The reason why I am asking is I have two contradictory pieces of information from two different articles. The first article titled "The validity ...
468 views

A property of unimodal sequences

It is well-known that $(-1)^j \sum_{i=0}^j (-1)^i\binom{n}{i} \geq 0$. This inequality can be used to prove Bonferroni's inequalities for example. Recently I noticed that a similar inequality applies ...
219 views

Bounding the series of the geometric means of the terms of a given positive series

Let $\{ a _ k \} _{k\in\mathbb{N} _ +}$ be a sequence of non-negative numbers, and let $MG(a_1,\dots,a_n)$ denote the geometric mean of the first $n$ terms. Then, the inequality  \sum _ {n\ge ...
423 views

What would the best treatment of Gehring's lemma look like?

In a course about elliptic regularity probably one sooner or later stubles into the reverse Holder inequalities, and has to introduce the Gehring lemma, which in one of its many versions improves a ...
I came across the following inequality, dubbed the "Neoclassical Inequality" which holds uniformly in $p\geq 1, n$: \$\frac{1}{p^2}\sum_{j=0}^n\frac{a^{j/p}b^{(n-j)/p}}{(j/p)!((n-j)/p)!}\leq ...