Let $~a\lt b\lt c\lt d$，proof that if $f$ is a convex function both in $[a,c]$ and $[b,d]$, $f$ is convex in $[a,d]$
116548
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).
6335
Proving that the set enclosed by an ellipse is convex
36371
Exercise on convex functions
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
119735
Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
74608
Convex function as supremum of countably many affine functions
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
26183
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
123732
Proving that the maximum of two convex functions is also convex
142922
How to prove that $e^x$ is convex?
4498
Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
142740
If $\varphi \in E'$ and $A$ is convex and open then $\varphi (A)$ is an open interval
113922
Proof that the intersection of any finite number of convex sets is a convex set
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?