About: Fixed-point theorems

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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 conditions on F that can be stated in general terms. Some authors claim that results of this kind are amongst the most generally useful in mathematics.

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rdfs:label	Fixed-point theorems (en) مبرهنة النقطة الثابتة (ar) Teorema del punt fix (ca) Fixpunktsatz (de) Teorema del punto fijo (es) Liste de théorèmes du point fixe (fr) Teoremi di punto fisso (it) 不動点定理 (ja) Teoria punktu stałego (pl) 不动点定理 (zh)
rdfs:comment	في الرياضيات، مبرهنة النقطة الثابتة تنص على أن دالة F ما تكون لها نقطة ثابتة (نقطة x حيث ) على الأقل، إذا ما توفرت شروط معينة حول F, يعبر عنها بشكل عام. (ar) En matemàtiques, el teorema del punt fix és un resultat que diu que una funció f tindrà almenys un (un punt x per al qual f (x) = x), per certes condicions de f que es poden definir en termes generals. (ca) Ein Fixpunktsatz ist in der Mathematik ein Satz, der unter gewissen Voraussetzungen die Existenz von Fixpunkten einer Abbildung garantiert. Das heißt, der Satz garantiert die Existenz eines Punktes mit . (de) 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 conditions on F that can be stated in general terms. Some authors claim that results of this kind are amongst the most generally useful in mathematics. (en) 数学における不動点定理（ふどうてんていり、英: fixed-point theorem）は、ある条件の下で自己写像 f: A → A は少なくとも 1 つの不動点（f(x) = x となる点 x ∈ A）を持つことを主張する定理の総称を言う。不動点定理は応用範囲が広く、分野を問わず様々なものがある。 (ja) In matematica, con teoremi di punto fisso ci si riferisce ai risultati che, in diversi contesti tra cui l'analisi matematica, la geometria o la topologia, mostrano l'esistenza di almeno un punto fisso per una qualche funzione definita in vari spazi. (it) Teoria punktu stałego (ang. fixed point theory) – dział matematyki, zajmujący się równaniami postaci f(x)=x, gdzie f jest pewną funkcją. Podstawowym zagadnieniem rozpatrywanym w teorii punktu stałego jest pytanie, przy jakich założeniach o zbiorze X (może to być przestrzeń topologiczna lub metryczna, zbiór uporządkowany i wiele innych) i o funkcji (może to być funkcja ciągła, kontrakcja, funkcja monotoniczna i wiele innych) równanie ma rozwiązanie. (Często też interesuje nas struktura zbioru rozwiązań tego równania.) Problem ten ma wiele wariantów, np. f może działać z pewnego podzbioru przestrzeni Banacha w całą tę przestrzeń (zob. np. ). (pl) 在数学中，不动点定理是一個結果表示函数F在某種特定情況下，至少有一個不动点存在，即至少有一个点x能令函数。在数学中有很多定理能保证函数在一定的条件下必定有一个或更多的不动点，而在这些最基本的定性结果当中存在不动点及其定理被应用的结果具有非常普遍的价值。 (zh) En analyse, un théorème du point fixe donne des conditions suffisantes d’existence d’un point fixe pour une fonction ou une famille de fonctions. Plus précisément, étant donné un ensemble E et une famille de fonctions f définies sur E et à valeurs dans E, ces théorèmes permettent de justifier qu’il existe un élément x de E tel que pour toutes les fonctions considérées on ait . Certains de ces théorèmes fournissent même un processus itératif permettant d’approcher un tel point fixe. (fr)
dcterms:subject	Iterative methods Fixed-point theorems Closure operators
Wikipage page ID	1011848 (xsd:integer)
Wikipage revision ID	1119434001 (xsd:integer)
Link from a Wikipage to another Wikipage	Bekić's theorem Denotational semantics Algebraic topology Injective metric space Computability theory Continuous function Iterative methods Mathematics Nielsen fixed-point theorem Church–Turing thesis Closure operator Function (mathematics) Bourbaki–Witt theorem Monotonic Cosine Complete lattice Parity (mathematics) Static program analysis Earle-Hamilton fixed-point theorem Euclidean space Finite set First-order logic Fixed point (mathematics) Banach fixed-point theorem Brouwer fixed-point theorem Browder fixed-point theorem Partial differential equation Caristi fixed-point theorem Diagonal lemma Discrete fixed-point theorem Fractal compression Iteration Kakutani fixed-point theorem Lefschetz fixed-point theorem Atiyah–Bott fixed-point theorem Fixed-point theorems Involution (mathematics) Abstract interpretation Closure operators Lambda calculus Collage theorem Don Zagier Borel fixed-point theorem Poset Sperner's lemma Fermat's theorem on sums of two squares Constructivism (philosophy of mathematics) Ordinal number Recursion (computer science) Set theory Kleene's recursion theorem Kleene fixed-point theorem Knaster–Tarski theorem Nielsen theory Poincaré–Birkhoff theorem Fixed-point combinator Fixed-point lemma for normal functions Fixed-point property Fixed-point theorems in infinite-dimensional spaces Schauder fixed-point theorem Unit ball Topological degree theory Ryll-Nardzewski fixed-point theorem Tychonoff fixed-point theorem
Link from a Wikipage to an external page	https://archive.org/details/fixedpoints0002shas https://archive.org/details/nonstandardmetho0000akso http://www.math-linux.com/spip.php%3Farticle60
sameAs	Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems Fixed-point theorems

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