Inequality for convex function $f:(0,\infty)\to\mathbb{R}$
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
86643
Convex function almost surely differentiable.
66151
Solving inequality for convex functions.
85153
Show that $f(x) = -\ln(x)$ is convex (WITHOUT using second derivative!)
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
78229
Proving that the tangent to a convex function is always below the function
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
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
144001
If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
16463
Is the function $\mbox{tr}(XAX')$ convex?
82371
$f$ is an entire function with Im $f\geq 0$
151410
Inequality of continuous functions
35857
Characterization of log-convexity
102959
Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$