Fixed-point theorem
one of several theorems stating that, under certain conditions, a function f will have an argument x for which f(x) = x
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 change
- 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