Show that $f$ has a fixed point at $\overline{B_1(0)}$.
12239
Holomorphic function with a fixed point
72889
Existence of fixed point given a mapping
133179
Fixed points under action of conjugate group elements
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
4636
How to show that $f$ is differentiable at $x=0.$
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
59717
Generalization of Banach's fixed point theorem
76790
Condition to guarantee $f=0$ on $[a,b]$
28191
How to show that a set of discontinuous points of an increasing function is at most countable
30455
Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
35133
Every increasing function from a certain set to itself has at least one fixed point
149564
Showing that a function is in $L^1$
17234
Show that a continuous function has a fixed point
33130
$f$ differentiable except in $1$ point
128975
Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$