New posts in Convex Analysis

Prove $\sqrt{x_1^2+4x_1x_2+5x_2^2+2x_1+6x_2+5}$ is convex

Is a broken (Euclidean) ball still convex?

The real function $f$ such that $\log \cdots \log (f)$ is strictly convex on its domain for any number of $\log$'s

Let $f$ be a real function and $a<b<c<d$. If $f$ is convex on $[a,c]$ and $[b,d]$, then can we say $f$ is convex on $[a,d]$?

Does this strong convexity estimate hold?

Gradient of $\mbox{dist}\left(x, D \right)^2:= \left\| x - P_{D}(x)\right\|_2^2$, where $P_{D}(x)$ is a projection operator

For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

When do three closed balls have a nonempty intersection?

Is this monotonicity property equivalent to convexity?

Does $f'(x)>\frac{f(x)}{x}$ for $x>0$ imply $f$ is convex?