$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
10727
Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
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
26388
proof that function is constant
153191
A function satisfy $x\frac{\partial f(x,y)}{\partial x}+y\frac{\partial f(x,y)}{\partial y}=0$ in a convex domain implies it is a constant
39921
show that f is constant on I
121771
Proof $f(x)\equiv 0$
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
27772
Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
145368
How to show $f:Y\to X^{+}$ is continuous?
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant