Given $|f(x) - f(y)| \leq 7(x-y)^2$ show $f$ is a constant function
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
68774
Proving that $f(x)$ is less than or equal to $1+\pi/4$
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
158407
derivative bounded by a constant multiple of the function
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
56127
Prove a function is constant under certain conditions
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
9451
Show bounded and convex function on $\mathbb R$ is constant
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
18734
Showing that a function is differentiable
105700
Proving $\,f$ is constant.
14067
If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C
135129
Proving an entire  function which misses a ball is constant
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$