Show that if $A$ is closed and $A+A=2A$ then A is convex.
106718
Prove if C is midpoint convex and closed then its a convex set
9451
Show bounded and convex function on $\mathbb R$ is constant
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
116223
Show that the angles satisfy $x+y=z$
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
116851
Show that f(x) is convex
149287
Prove that $A,B>0$ and $A_{ij}0$
60521
Continuity of a convex function
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
113922
Proof that the intersection of any finite number of convex sets is a convex set
110845
Convex Set with Empty Interior Lies in an Affine Set
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$