Show that $f$ is constant.
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
54729
Prove that $f$ has a fixed point .
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
3818
Proving two entire functions are constant.
96539
is $f$ constant or dilation
143491
Show that $f$ is differentiable on $(−1, 1)$.
5416
How does one prove if a multivariate function is constant?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
58664
Proving a function is continuous for a fixed variable
142138
Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
101700
Liouvilles theorem question - show $f$ is constant
9451
Show bounded and convex function on $\mathbb R$ is constant
150554
proof that $f'$ is continuous at $a$
88586
show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant