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

some conditions on F that can be stated in general terms. The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied...

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

the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan Banach was born on 30 March...

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...

Juliusz Schauder (a previous result in a different vein, the Banach fixed-point theorem for contraction mappings in complete metric spaces was proved...

result saying that at least one fixed point exists, under some general condition. For example, the Banach fixed-point theorem (1922) gives a general criterion...

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...

Banach fixed-point theorem proves that a solution can be obtained by fixed-point iteration of successive approximations. In this context, this fixed-point...

type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. We have the following chain of strict inclusions for functions...

contraction mapping to which the Banach fixed-point theorem can be applied. Let D be a connected open subset of a complex Banach space X and let f be a holomorphic...

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...

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...

similar to the form of the Banach fixed-point theorem, although it states existence and uniqueness of a zero rather than a fixed point. Newton's method constructs...

Banach's fixed point theorem, which relies on the Cauchy completeness. That part of the argument is replaced by the use of the extreme value theorem,...

solution is a fixed point of the operator. The Banach fixed point theorem is then invoked to show that there exists a unique fixed point, which is the...

subset Pointwise convergence Metrization theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic...

fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point...

diverges Banach fixed-point theorem Banach–Tarski paradox Basel problem Bolzano–Weierstrass theorem Brouwer fixed-point theorem Buckingham π theorem (proof...

fixed-point computation was the fixed-point iteration algorithm of Banach. Banach's fixed-point theorem implies that, when fixed-point iteration is applied to...

Malgrange–Ehrenpreis theorem (differential equations) Autonomous convergence theorem (dynamical systems) Banach fixed-point theorem (metric spaces, differential...

fixed points are guaranteed to exist and fixed-point iteration is guaranteed to converge, although possibly slowly, by the Banach fixed-point theorem...

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)...

result of a computation (which can be guaranteed to exist by the Banach fixed-point theorem). Similar ideas can be found in domain theory. p-adic analysis...

interior. The Banach fixed-point theorem states that a contraction mapping on a complete metric space admits a fixed point. The fixed-point theorem is often...

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists...

see the Jordan curve theorem. If S {\displaystyle S} is a subset of a Euclidean space, then x {\displaystyle x} is an interior point of S {\displaystyle...

turbulence data. Mathematics portal Systems science portal Banach fixed point theorem – Theorem about metric spacesPages displaying short descriptions of...

Mathematical set whose closure has empty interior Lebesgue's density theorem – Theorem in analysis, for measure-theoretic characterization and properties...

Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th...