Elementary questions about functions, notation, properties, and operations such as function composition.

learn more… | top users | synonyms (1)

10
votes
1answer
225 views
+100

$f(nx)\to 0$ as $n\to+\infty$

Let $f:\mathbb R^+\to\mathbb R^+$ be a continuous function that has the following property: For any $x\in I$, $f(nx)\to 0$ as $n\to+\infty$. Intuitively, if $I$ is 'big' enough, $f$ necessarily ...
2
votes
1answer
33 views
+50

Jensen-like averaging inequality on integers

Let $\mathbb{Z}^*=\mathbb{Z}^+\cup\{0\}$. Let $f:\mathbb{Z}^*\rightarrow\mathbb{R}$ be a nondecreasing function such that $f(a+b)\leq f(a)+f(b)$ for all $a,b\in\mathbb{Z}^*$. Is it true that for all ...