Is there a convex function smaller than a given function.
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
16463
Is the function $\mbox{tr}(XAX')$ convex?
151981
Tangent line of a convex function
40403
Show that the function is convex
73074
$f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
107321
How to show convexity of a ball in metric space?
72659
How can we define convexity in one dimension?
130049
Converse of Jensen's inequality
20614
Example of a function such that $\varphi\left(\frac{x+y}{2}\right)\leq \frac{\varphi(x)+\varphi(y)}{2}$ but $\varphi$ is not convex
85153
Show that $f(x) = -\ln(x)$ is convex (WITHOUT using second derivative!)
138959
On the equality case of the Hölder and Minkowski inequalities
8963
Function that is both midpoint convex and concave
77217
Proof that a coordinate-wise convex function is convex?
87207
Prove that the support function of an arbitrary set $A\subset\mathbb R^n$ is convex
66151
Solving inequality for convex functions.
2848
Convex integral inequality
116548
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).