Example of nonconvex function with nonempty subgradient
64197
Subgradients of non-convex functions
38695
Inverse of Strictly Monotone Function
62817
Functions which are Continuous, but not Bicontinuous
124861
The extension of smooth function
60521
Continuity of a convex function
28315
Monotone functions and non-vanishing of derivative
73074
$f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
53376
A continuous, nowhere differentiable but invertible function?
135867
$f(x)=x^3$ is convex nor concave without to derivate
58816
Existence of a continuous function which does not achieve a maximum.
112404
Eliminating discontinuities for increasing function
109732
Nowhere continuous function limit
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
112548
Existence of non-trivial linear functional on any vector space
8963
Function that is both midpoint convex and concave
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?