Fixed point of $f\circ f$ when $f$ is entire and not a translation
90685
The composition of non-linear entire functions with no fixed points has infinitely many fixed points.
107072
Schwarz's Lemma, fixed points question
61884
If $T^n$ is $q$-contractive, $T$ exactly has one fixed point
24126
When functions commute under composition
34836
Composition of Absolutely Continuous Functions
42638
Showing that a function $f$ has a unique fixed point in a metric space.
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
39321
If $f:\mathbb R \to \mathbb R$ satisfies $f'(x) <L$ for some $L<1$, then $f$ has a unique fixed point
126842
Fixed point in a continuous function
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
63701
An example of a regular function over an open set
2527
Entire function bounded by a polynomial is a polynomial
129875
Fixed point theorem on spheres
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
14830
A transformation of F[x]
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation