If $f(1) = i$ what is $f(i)$ for a function with $|f(z)| \leq K|z|$ ? GATE 2011
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
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
77074
If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
82229
Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
31522
Proving $f$ has at least one zero inside unit disk
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
35556
$f(z)=\frac{z}{1+|z|} $ Is 1-1?
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
50552
find functions that $f(m+k)=f(mk-n)$
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
21954
A question about $f(x)\equiv 0$