What is 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 (mathematics)|lemma]], for making [[First-order logic|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]]