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Fixed-point theorem facts for kids

Kids Encyclopedia Facts

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
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