Fixed-point theorem

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

Category:Mathematical theorems