Find all continuous functions that satisfy the Jensen inequality(?) $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}$
8963
Function that is both midpoint convex and concave
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
71738
Continuously differentiable function iff $|f(x + h) - f(x + t) - l(h - t)| \leq \epsilon |h-t|$
28822
$|x| - |y| \leq |x-y|?$
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
44607
Prove that a continuous function on a closed interval attains a maximum
130049
Converse of Jensen's inequality
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
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
66151
Solving inequality for convex functions.
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
23294
Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line