query: $x \rightarrow |x|^p$ is strictly convex
positive_passages.docid: 25017
positive_passages.text: Why is every $p$-norm convex?
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
negative_passages.docid: 64239
negative_passages.text: Upper Bound for $p(1-p) $ where $0 \le p \le 1$
negative_passages.docid: 73074
negative_passages.text: $f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
negative_passages.docid: 55866
negative_passages.text: Convex + Monotone =? Convex
negative_passages.docid: 123732
negative_passages.text: Proving that the maximum of two convex functions is also convex
negative_passages.docid: 33527
negative_passages.text: Star convex set is simply connected.
negative_passages.docid: 115930
negative_passages.text: Is every convex function on an open interval continuous?
negative_passages.docid: 40905
negative_passages.text: 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
negative_passages.docid: 134384
negative_passages.text: What does $\rightarrow$ mean in $p \rightarrow q$
negative_passages.docid: 48792
negative_passages.text: Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$
negative_passages.docid: 147420
negative_passages.text: Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
negative_passages.docid: 6335
negative_passages.text: Proving that the set enclosed by an ellipse is convex
negative_passages.docid: 10352
negative_passages.text: Prove that $x^n$ is a convex function on $(0,\infty)$
negative_passages.docid: 77217
negative_passages.text: Proof that a coordinate-wise convex function is convex?
negative_passages.docid: 137511
negative_passages.text: Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
negative_passages.docid: 15645
negative_passages.text: Is convex open set in $\mathbb{R}^n$ is regular?