Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex
67313
Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
116382
Showing convexity of a function with the restriction over an arbitrary line
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
57514
The Minkowski sum of two convex sets is convex
25171
Why does a convex set have the same interior points as its closure?
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
60521
Continuity of a convex function
106718
Prove if C is midpoint convex and closed then its a convex set
116851
Show that f(x) is convex
97584
How to prove this property using convexity?
131596
Symmetric Inequality in $\mathbb{R}$
63529
How to show that this set is compact in $\ell^2$
138457
Seminorms: Absolute Convexity
36371
Exercise on convex functions
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave