the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some...

In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X...

In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued...

The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to locally convex topological vector spaces, which may be of infinite...

In mathematics, Lawvere's fixed-point theorem is an important result in category theory. It is a broad abstract generalization of many diagonal arguments...

In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for...

the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following: Kleene Fixed-Point Theorem. Suppose ( L...

the theorem in particular guarantees the existence of at least one fixed point of f, and even the existence of a least fixed point (or greatest fixed point)...

have a fixed point, but it doesn't describe how to find the fixed point. The Lefschetz fixed-point theorem (and the Nielsen fixed-point theorem) from algebraic...

rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent...

neutrally stable fixed point. Multiple attracting points can be collected in an attracting fixed set. The Banach fixed-point theorem gives a sufficient...

Metamathematics. A related theorem, which constructs fixed points of a computable function, is known as Rogers's theorem and is due to Hartley Rogers...

fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Continuous fixed-point theorems often...

mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed-point theorem for maps of a complete...

closely related argument from algebraic topology, using the Lefschetz fixed-point theorem. Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0, ... the...

In mathematics, a Hausdorff space X is called a fixed-point space if it obeys a fixed-point theorem, according to which every continuous function f :...

Many fixed-point theorems yield algorithms for locating the least fixed point. Least fixed points often have desirable properties that arbitrary fixed points...

mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed-point theorem for partially ordered sets...

In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping...

Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth...

theorem can be proved from the Brouwer fixed point theorem (in 2 dimensions), and the Brouwer fixed point theorem can be proved from the Hex theorem:...

fallback The assumption on "nonempty" has meaning: a fixed point theorem often states the set of fixed point is an Hadamard space. The main content of such...

functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if E {\displaystyle E} is a normed vector space and K...

Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan Banach...

The Browder fixed-point theorem is a refinement of the Banach fixed-point theorem for uniformly convex Banach spaces. It asserts that if K {\displaystyle...

In mathematics, the Markov–Kakutani fixed-point theorem, named after Andrey Markov and Shizuo Kakutani, states that a commuting family of continuous affine...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same...

instance in Lefschetz's fixed-point theorem. The Lefschetz number is a useful tool to find out whether a continuous function admits fixed-points. This data...