Let $f:\mathbb{R}^n\rightarrow ]-\infty,+\infty]$ be proper and strictly convex.
48490
Examples of $f$ strictly convex, either with one minimizer or with no minimizer.
125175
convexity proof of a function including ln and sums
117716
Condition on function $f:\mathbb{R}\rightarrow \mathbb{R}$ so that $(a,b)\mapsto | f(a) - f(b)|$ generates a metric on $\mathbb{R}$
115814
If $\operatorname{Re}f^\prime > 0$ on a convex domain, then $f$ is one-to-one.
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
102959
Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
48990
Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
150572
Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
31548
Proof of "every convex function is continuous"
121886
Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
142812
Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$
156101
Is the convex hull of closed set in $\mathbb R^{n}$ is closed?