If $|f(x)-f(y)|<(x-y)^2$ for all $x,y \in \mathbb{R}$. Then $f(x)$ is constant.
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
62640
Show a given analytic function is constant
47474
Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
45222
When $f(x) = g(y)$ for almost every $(x,y)$, must $f$ and $g$ be constant almost everywhere?
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
97371
Proving a function is constant, under certain conditions?
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
93270
is that function must be constant under the following conditions
137043
To show that function is constant
145368
How to show $f:Y\to X^{+}$ is continuous?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
158561
Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$