Category

Fixed-point theorems

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Banach fixed-point theorem

theorem about metric spaces

Brouwer fixed-point theorem

every continuous function on a compact set has a fixed point

Borsuk–Ulam theorem

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

Kakutani fixed-point theorem

theorem that a function f: S→Pow(S) on a compact nonempty convex subset S⊂ℝⁿ, whose graph is closed and whose image f(x) is nonempty and convex for all x∈S, has a fixed point

Knaster–Tarski theorem

theorem in order and lattice theory

Lefschetz fixed-point theorem

fixed-point iteration

root-finding algorithm

Sperner's lemma

lemma that every Sperner coloring of a triangulated simplex contains a properly colored simplex

Schauder fixed point theorem

theorem that a continuous mapping of a convex subset of a topological vector space into a compact subset of itself has a fixed point

Kleene fixed-point theorem

Theorem in order theory

Caristi fixed-point theorem

Poincaré–Birkhoff theorem

in symplectic topology, the theorem that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points

Ryll-Nardzewski fixed-point theorem

mathematical branch

Knaster–Kuratowski–Mazurkiewicz lemma

Markov–Kakutani fixed-point theorem