Prove that a function is constant
97371
Proving a function is constant, under certain conditions?
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
9451
Show bounded and convex function on $\mathbb R$ is constant
727
Prove that any continuous integer-valued function of a real variable is constant.
105172
Prove that the entire function is constant over certain conditions.
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?
100740
proof of that a continuous function has a fixed point
101700
Liouvilles theorem question - show $f$ is constant
40208
Locally Constant Functions on Connected Spaces are Constant
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
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?
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
62640
Show a given analytic function is constant
53627
Proving continuity of $f$
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant