If $f^N$ is contraction function, show that $f$ has precisely one fixed point.
61884
If $T^n$ is $q$-contractive, $T$ exactly has one fixed point
149999
fixed point of a continuous map on a projective space
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
100740
proof of that a continuous function has a fixed point
84004
Prove there is no contraction mapping from compact metric space onto itself
126842
Fixed point in a continuous function
150373
Number of Fixed Point(s) of a Differentiable Function
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
118048
Can a function with just one point in its domain be continuous?
105594
Fixed point, union of $\aleph_0, \aleph_{\aleph_0},\aleph_{\aleph_{\aleph_0}}\dots$ [see Noah's comment on notation]
37331
Prove that every set with more than one element has a permutation without fixed points
75227
If $S=\{1,2,\dots,n\}$ and $P_n(k)$ be the number of permutations of $S$ having $k$ fixed points, then $\sum_{k=0}^nk.P_{n}(k)=n!$
58664
Proving a function is continuous for a fixed variable
17234
Show that a continuous function has a fixed point
11322
Show that $f$ vanishes identically.
35133
Every increasing function from a certain set to itself has at least one fixed point
99827
For what values will f(x) be necessarily one-one?