if $|f(x)-f(y)|\le |x-y|^{\sqrt 2}$ then is $f$ a constant function?
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
23615
Why does zero derivative imply a function is locally constant?
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
101700
Liouvilles theorem question - show $f$ is constant
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
10564
$f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
154742
If $f(z)$ analytic in the domain $D$ and $f'(z)=0$ so $f(z)=$constant?
31327
Why is $\sqrt{x}$ a function?
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
82001
How to prove the function is a constant
56127
Prove a function is constant under certain conditions
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant