Fixed-point theorem facts for kids

In mathematics, a fixed-point theorem is a theorem that a mathematical function has a fixed point. At that fixed point, the function's input and output are equal.

This concept is not one theorem itself; it is a way to describe many other theorems.

List of fixed-point theorems

Atiyah–Bott fixed-point theorem
Banach fixed-point theorem
Borel fixed-point theorem
Browder fixed-point theorem
Brouwer fixed-point theorem
Caristi fixed-point theorem
Diagonal lemma, also called the fixed-point lemma, for making logical sentences that describe themselves.
Fixed-point lemma for normal functions
Fixed-point property
Injective metric space
Kakutani fixed-point theorem
Kleene fixpoint theorem
Knaster–Tarski theorem
Lefschetz fixed-point theorem
Nielsen fixed-point theorem
Poincaré–Birkhoff theorem proves that a function has two fixed points
Ryll-Nardzewski fixed-point theorem
Schauder fixed-point theorem
Topological degree theory
Tychonoff fixed-point theorem