How to show $P = \{(x,y)\in \mathbb{R}^2:xy\ge3, x,y\ge0\}$ is convex?
67313
Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
116548
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).
147420
Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
71619
Proving that a convex function is Lipschitz
108704
Help with proof of $|x+y| \geq |x|-|y|$
116851
Show that f(x) is convex
25171
Why does a convex set have the same interior points as its closure?
24230
Proof that CRF models and logistic models are convex functions
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
144001
If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex
15645
Is convex open set in $\mathbb{R}^n$ is regular?
135867
$f(x)=x^3$ is convex nor concave without to derivate
58988
Composition of convex function and affine function
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
142142
Show that a convex polygon is contained within the largest circle determined by three consecutive vertices
60521
Continuity of a convex function
6335
Proving that the set enclosed by an ellipse is convex