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 :...

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

{\displaystyle x,y\in X.} Banach fixed-point theorem. Let ( X , d ) {\displaystyle (X,d)} be a non-empty complete metric space with a contraction mapping T...

convex compact subset K {\displaystyle K} of Euclidean space to itself. Among hundreds of fixed-point theorems, Brouwer's is particularly well known, due...

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 numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function f {\displaystyle...

ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (see also Sperner's lemma). For...

In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation...

the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X {\displaystyle...

is most commonly used to describe topological spaces on which every continuous mapping has a fixed point. But another use is in order theory, where a partially...

subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization...

Raum means both room and space in German. Fixed-point space – Space where all functions have fixed points, a Hausdorff space X such that every continuous...

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...

No Fixed Point in Space is the third studio album by English musician Jack Cooper's music project Modern Nature. It was released on 29 September 2023 by...

In probability theory, the KPZ fixed point is a Markov field and conjectured to be a universal limit of a wide range of stochastic models forming the...

In physics, an infrared fixed point is a set of coupling constants, or other parameters, that evolve from arbitrary initial values at very high energies...

holomorphic mapping of an open domain in a complex Banach space into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and Richard...

Banach fixed-point theorem for maps of a complete metric space into itself. Caristi's fixed-point theorem modifies the ε {\displaystyle \varepsilon } -variational...

compact convex subset in a locally convex topological vector space has a common fixed point. This theorem is a key tool in one of the quickest proofs of...

function f(z) − z at the point z0. In real Euclidean space, the fixed-point index is defined as follows: If x0 is an isolated fixed point of f, then let g be...

In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development...

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

motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have...

In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate...

remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry (preserves distance). In the Euclidean plane, a point reflection...

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

Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an affine subspace of the vector space. One commonly...

satellites are used; the given position may be a specified fixed point or any fixed point within specified areas; in some cases this service includes...

surface in three-dimensional space formed from the union of infinite lines that pass through a fixed point and a space curve. A (general) conical surface...

Two simple attractors are a fixed point and the limit cycle. Attractors can take on many other geometric shapes (phase space subsets). But when these sets...