Contraction principle

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

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Contraction principle (large deviations theory) — In mathematics specifically, in large deviations theory the contraction principle is a theorem that states how a large deviation principle on one space pushes forward to a large deviation principle on another space via a continuous function.… … Wikipedia
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Length contraction — Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non zero velocity relative to that observer. This contraction (more formally called Lorentz … Wikipedia
Muscle contraction — See also: Twitch and Tremor Top down view of skeletal muscle Muscle fiber generates tension through the action of actin and myosin cross bridge cycling. While under tension, the muscle may lengthen, shorten, or … Wikipedia
Bernoulli's principle — This article is about Bernoulli s principle and Bernoulli s equation in fluid dynamics. For Bernoulli s Theorem (probability), see Law of large numbers. For an unrelated topic in ordinary differential equations, see Bernoulli differential… … Wikipedia
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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
Rate function — In mathematics mdash; specifically, in large deviations theory mdash; a rate function is a function used to quantify the probabilities of rare events. It is required to have several nice properties which assist in the formulation of the large… … Wikipedia
Large deviations theory — In Probability Theory, the Large Deviations Theory concerns the asymptotic behaviour of remote tails of sequences of probability distributions. Some basic ideas of the theory can be tracked back to Laplace and Cramér, although a clear unified… … Wikipedia

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Contraction principle

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