$f$ convex and concave, then $f=ax+b$
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
151981
Tangent line of a convex function
7825
If $f$ is a concave function and $f(0) \geq 0$ then $f(a+b) \leq f(a) + f(b)$ for all $a,b >0$
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
40905
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
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
14448
Elementary proof that $|x|^p$ is convex.
135867
$f(x)=x^3$ is convex nor concave without to derivate
16943
Midpoint-Convex and Continuous Implies Convex
77217
Proof that a coordinate-wise convex function is convex?
125175
convexity proof of a function including ln and sums
138457
Seminorms: Absolute Convexity
116548
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).
73074
$f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
78229
Proving that the tangent to a convex function is always below the function
6335
Proving that the set enclosed by an ellipse is convex
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$