Prove that $f:[0,\infty) \to \mathbb{R}, x\mapsto x^p$ for $p\geq 1$ is convex.
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
106718
Prove if C is midpoint convex and closed then its a convex set
40905
Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
116851
Show that f(x) is convex
60521
Continuity of a convex function
135867
$f(x)=x^3$ is convex nor concave without to derivate
597
f is differentiable on convex domain D and Re(f')>0 implies f is injective on D
52231
Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
56081
Prove that the ellipsoid $E = \{ (x,y,z) \in R^3 \mid \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} \leq 1 \}$ is convex
81112
Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
97584
How to prove this property using convexity?
30423
interior points and convexity