Proof using the fixed point theorem
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
156877
Rank-one perturbation proof
83784
Fixed Point of $x_{n+1}=i^{x_n}$
8039
an analytic function from unit disk to unit disk with two fixed point
144713
Simple Calculus Proof
154459
Constructing a HoTT proof term of 1≠0
99726
Proving that a function is not a contraction
91482
Is there a short proof for the Intermediate Value Theorem
36402
Prove that $f(x) = \cos(x)$ has a unique fixed point.
17234
Show that a continuous function has a fixed point
120065
Niven’s theorem proof.
148500
Understanding this theorem and how to go about proving it surjectivity?
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
72889
Existence of fixed point given a mapping
105700
Proving $\,f$ is constant.
74352
A weak version of Markov-Kakutani fixed point theorem
126632
Proving Inequalities with Absolute values