Prove that a function is a constant multiple of the other
42487
$f(z)$ and $g(z)$ are Meromorphic functions such $|f(z)|\le|g(z)|$ for all $z\in\mathbb{C} $ then $ f=ag$
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
114245
What might I use to show that an entire function with positive real parts is constant?
60348
How do I prove $F(a)=F(a^2)?$
97371
Proving a function is constant, under certain conditions?
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
132478
Prove that continuous functions mapping irrationals to rationals must be constant
99726
Proving that a function is not a contraction
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
115636
Show that $f$ is either injective or a constant function.
33617
Prove the inequality involving multiple integrals
58664
Proving a function is continuous for a fixed variable
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
141529
Proving existence of a minimum
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.