- contraction mapping
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contraction mapping
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Contraction mapping — In mathematics, a contraction mapping, or contraction, on a metric space (M,d) is a function f from M to itself, with the property that there is some nonnegative real number k < 1 such that for all x and y in M, The smallest such value of k is … Wikipedia
Contraction — may refer to: In physiology: Muscle contraction, one that occurs when a muscle fiber lengthens or shortens Uterine contraction, contraction of the uterus, such as during childbirth Contraction, a stage in wound healing In linguistics: Synalepha,… … Wikipedia
Contraction principle — In mathematics, contraction principle may refer to: the Banach fixed point theorem, also known as the contraction mapping theorem/principle; the contraction principle in large deviations theory This disambiguation page lists mathematics articles… … Wikipedia
Banach fixed-point theorem — In mathematics, the Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of… … Wikipedia
Banach fixed point theorem — The Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… … Wikipedia
Brouwer fixed point theorem — In mathematics, the Brouwer fixed point theorem is an important fixed point theorem that applies to finite dimensional spaces and which forms the basis for several general fixed point theorems. It is named after Dutch mathematician L. E. J.… … Wikipedia
Comparametric equation — A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter. For example, ƒ(2t) = 4ƒ(t) is a comparametric… … Wikipedia
Schwarz–Ahlfors–Pick theorem — In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half plane model. It states that the Poincaré metric is distance decreasing on harmonic functions.The theorem… … Wikipedia
Ricci decomposition — In semi Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a pseudo Riemannian manifold into pieces with useful individual algebraic properties. This decomposition is of fundamental importance in… … Wikipedia
