Caristi fixed-point theorem (original) (raw)
Le théorème du point fixe de — ou de Caristi– (en) — est un théorème de topologie générale qui étend le théorème du point fixe de Banach-Picard, en garantissant l'existence de points fixes pour une plus large classe d'applications d'un espace métrique complet dans lui-même. Il est équivalent à une forme faible du principe variationnel d'Ekeland.
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| dbo:abstract | In 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 metric space into itself. Caristi's fixed-point theorem modifies the ε-variational principle of Ekeland (1974, 1979). The conclusion of Caristi's theorem is equivalent to metric completeness, as proved by Weston (1977). The original result is due to the mathematicians and William Arthur Kirk. Caristi fixed-point theorem can be applied to derive other classical fixed-point results, and also to prove the existence of bounded solutions of a functional equation. (en) Le théorème du point fixe de — ou de Caristi– (en) — est un théorème de topologie générale qui étend le théorème du point fixe de Banach-Picard, en garantissant l'existence de points fixes pour une plus large classe d'applications d'un espace métrique complet dans lui-même. Il est équivalent à une forme faible du principe variationnel d'Ekeland. (fr) De dekpuntenstelling van Caristi is door het geringe aantal eisen dat wordt gesteld zeer geschikt om het bestaan van dekpunten aan te tonen, daar waar andere dekpuntstellingen falen. De stelling is niet constructief en garandeert niet de uniciteit van het dekpunt. (nl) カリスティの不動点定理（カリスティのふどうてんていり、英: Caristi fixed-point theorem）あるいはカリスティ＝カークの不動点定理（Caristi-Kirk fixed-point theorem）と呼ばれる定理は、数学において、バナッハの不動点定理を完備距離空間からそれ自身への写像に対して一般化するものである。カリスティの不動点定理は、（1974,1979）の ε-を少し変えたものである。また、カリスティの定理の結論が距離完備性と同値であることは Weston (1977) によって示された。元々の結果は、数学者ジェームス・カリスティとによるものである。 (ja) In matematica, il teorema di Caristi o teorema di Caristi-Kirk è un teorema di punto fisso che generalizza il teorema delle contrazioni per applicazioni di uno spazio metrico completo in sé. Si tratta di una variante dell'ε-principio variazionale di (1974, 1979). Inoltre, la conclusione del teorema di Caristi è equivalente alla completezza metrica, come dimostrato da Weston (1977). Il risultato originale è dovuto ai matematici e . (it) |
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| rdfs:comment | Le théorème du point fixe de — ou de Caristi– (en) — est un théorème de topologie générale qui étend le théorème du point fixe de Banach-Picard, en garantissant l'existence de points fixes pour une plus large classe d'applications d'un espace métrique complet dans lui-même. Il est équivalent à une forme faible du principe variationnel d'Ekeland. (fr) De dekpuntenstelling van Caristi is door het geringe aantal eisen dat wordt gesteld zeer geschikt om het bestaan van dekpunten aan te tonen, daar waar andere dekpuntstellingen falen. De stelling is niet constructief en garandeert niet de uniciteit van het dekpunt. (nl) カリスティの不動点定理（カリスティのふどうてんていり、英: Caristi fixed-point theorem）あるいはカリスティ＝カークの不動点定理（Caristi-Kirk fixed-point theorem）と呼ばれる定理は、数学において、バナッハの不動点定理を完備距離空間からそれ自身への写像に対して一般化するものである。カリスティの不動点定理は、（1974,1979）の ε-を少し変えたものである。また、カリスティの定理の結論が距離完備性と同値であることは Weston (1977) によって示された。元々の結果は、数学者ジェームス・カリスティとによるものである。 (ja) In matematica, il teorema di Caristi o teorema di Caristi-Kirk è un teorema di punto fisso che generalizza il teorema delle contrazioni per applicazioni di uno spazio metrico completo in sé. Si tratta di una variante dell'ε-principio variazionale di (1974, 1979). Inoltre, la conclusione del teorema di Caristi è equivalente alla completezza metrica, come dimostrato da Weston (1977). Il risultato originale è dovuto ai matematici e . (it) In 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 metric space into itself. Caristi's fixed-point theorem modifies the ε-variational principle of Ekeland (1974, 1979). The conclusion of Caristi's theorem is equivalent to metric completeness, as proved by Weston (1977). The original result is due to the mathematicians and William Arthur Kirk. (en) |
| rdfs:label | Satz von Caristi (de) Caristi fixed-point theorem (en) Théorème du point fixe de Caristi (fr) Teorema di Caristi (it) カリスティの不動点定理 (ja) Dekpuntstelling van Caristi (nl) |
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