Teorema do ponto fixo de Schauder

O Teorema do ponto fixo de Schauder é uma generalização do teorema do ponto fixo de Brouwer. Enquanto o teorema de Brouwer se aplica a espaços euclidianos, o teorema de Schauder vale em espaços de Banach. Este resultado foi conjecturado e provado em casos especiais [como os espaços de Banach] por Julius Schauder, em 1930.

Enunciado

Seja um espaço de Banach, um fechado, limitado e convexo não vazio e um operador compacto. Então admite um ponto fixo , ou seja:

Versão Alternativa

Seja um espaço de Banach, um compacto e convexo e uma função contínua. Então admite um ponto fixo , ou seja:

Observações

  • Quando tem dimensão finita, então este teorema é idêntico ao teorema do ponto fixo de Brouwer, pois, então, um conjunto é compacto se e somente se for limitado e fechado.
  • A generalização deste resultado é o Teorema do Ponto-Fixo de Schauder-Tychonoff, no qual o russo Andrei Tychonoff foi o primeiro a provar este caso generalizado em 1934 - Enunciado: o teorema estabelece que uma função contínua definida num subconjunto compacto e convexo de um espaço vetorial topológico localmente convexo possui um ponto fixo.
  • Andrey Markov usou este "teorema de Schauder" para provar o seu teorema do ponto fixo, em 1936. E depois, já em 1938, o matemático nipo-americano Shizuo Kakutani generalizou o resultado de Markov e, assim, o resultado geral é denominado "Teorema do Ponto Fixo de Markov-Kakutani".

Referências

  • Dugundji, James. Topology. 1aedição. Boston: Allyn and Bacon, 1965
  • Evans, C. Lawrence. Partial Differential Equations. 3aedição. Providence, RI: AMS, 2002
  • Zeidler, Eberhard. Nonlinear Functional Analysis and its Applications.vol.I.Fixed-Point Theorems. 1aedição. Springer-Verlag New York Inc., 1986

Read other articles:

Kampanye Menglianggu

Kampanye MengliangguBagian dari Perang Saudara TiongkokTanggal13–16 Mei 1947LokasiShandong, TiongkokHasil Kemenangan Tentara Pembebasan RakyatPihak terlibat Tentara Revolusioner Nasional Tentara Pembebasan RakyatTokoh dan pemimpin Gu Zhutong Tang Enbo Zhang Lingfu † Huang Baitao Qiu Qingquan Hu Lien Su Yu Chen YiKekuatan 600.000 200.000Korban 14.000 gugur18.000 tertangkap 3.500 gugur7.500 terluka Kampanye Menglianggu (孟良崮战役) adalah sebuah kampanye pertempuran antara nasiona...

 

Elvira Madigan (película de Bo Widerberg)

Elvira Madigan Ficha técnicaDirección Bo WiderbergProducción Waldemar BergendahlGuion Bo WiderbergMúsica Ulf BjörlinFotografía Jörgen PerssonJörgen PerssonMontaje Bo WiderbergProtagonistas Pia DegermarkThommy BerggrenYvonne Ingdal Ver todos los créditos (IMDb)Datos y cifrasPaís SueciaAño 1967Género Cine biográfico, romance y dramaDuración 91 minutosIdioma(s) DanésCompañíasDistribución NetflixFicha en IMDbFicha en FilmAffinity[editar datos en Wikidata] Elvira Madiga...

 

Charlot Salwai

Charlot SalwaiSalwai pada bulan November 2016 Perdana Menteri Vanuatu ke-11PetahanaMulai menjabat 6 Oktober 2023PresidenNikenike Vurobaravu PendahuluSato KilmanPenggantiPetahanaMasa jabatan11 Februari 2016 – 20 April 2020PresidenBaldwin LonsdaleEsmon Saimon (Penjabat)Tallis Obed MosesWakilJotham Napat PendahuluSato KilmanPenggantiBob Loughman Informasi pribadiLahir24 April 1963 (umur 60)Pulau Pentakosta, Hebrides BaruPartai politikGerakan Reunifikasi untuk PerubahanSua...

Bunga Dahlia

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Januari 2023. Bunga DahliaAlbum studio karya O. M. PengabdianDirilis1984GenreDangdutLabelIndra Records Bunga Dahlia adalah sebuah album Dangdut milik grup musik O. M. Pengabdian pimpinan Alwi Hasan yang dirilis tahun 1984. Daftar lagu Bunga Dahlia - Su'udiah Jan...

 

Cucuteni

For other uses, see Cucuteni (disambiguation). Commune in Iași, RomaniaCucuteniCommuneArchaeological Reserve of CucuteniLocation in Iași CountyCucuteniLocation in RomaniaCoordinates: 47°16′N 26°56′E / 47.267°N 26.933°E / 47.267; 26.933CountryRomaniaCountyIașiGovernment • Mayor (2020–2024) Pamfilică Brânză[1] (PSD)Area28.22 km2 (10.90 sq mi)Elevation228 m (748 ft)Population (2021-12-01)[2]1,10...

 

Jussieu Peninsula

For other uses, see Jussieu. Place in South AustraliaJussieu PeninsulaSouth AustraliaCurta Rocks, South AustraliaJussieu PeninsulaCoordinates34°51′18″S 135°52′42″E / 34.855108°S 135.878459°E / -34.855108; 135.878459[1] Mean max temp Mean min temp Annual rainfall 21.2 °C 70 °F 11.3 °C 52 °F 383.2 mm 15.1 in FootnotesClimate[2] Jussieu Peninsula is a peninsula located at the south east end of Eyre Peninsula in South Australia. It is bounde...

New Skin for the Old Ceremony

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: New Skin for the Old Ceremony – news · newspapers · books · scholar · JSTOR (July 2014) (Learn how and when to remove this template message) 1974 studio album by Leonard CohenNew Skin for the Old CeremonyStudio album by Leonard CohenReleasedAugust ...

 

Vickers Vimy

Vickers Vimy, Pesawat Pengebom Inggris untuk Perang Dunia I pada tahun 1918 Vickers Vimy F.B.27 dikenal sebagai pesawat pertama yang melakukan penerbangan tanpa henti melintasi Samudra Atlantik.[1] Vickers Vimy pada mulanya dibuat sebagai pesawat pengebom yang dirancang mampu meluncurkan serangan hingga ke Berlin, Jerman. Pertama kali diterbangkan pada 30 November 1917. Pada Juli 1919, pesawat Vimy dimasukkan dalam armada Royal Air Force (Angkatan Udara Inggris).[2] Pesawat in...

 

Juan Yepez

Venezuelan baseball player (born 1998) Baseball player Juan YepezYepez with the Palm Beach Cardinals in 2019Washington Nationals Outfielder / First basemanBorn: (1998-02-19) February 19, 1998 (age 26)Caracas, VenezuelaBats: RightThrows: RightMLB debutMay 4, 2022, for the St. Louis CardinalsMLB statistics (through 2023 season)Batting average.240Home runs14Runs batted in32 Teams St. Louis Cardinals (2022–2023) Juan David Yepez (born February 19, 1998) is a Venezuelan profe...

County di Kroasia

Kabupaten di KroasiaHrvatske županije (Kroasia)Kabupaten-kabupaten di Kroasia:   Bjelovar-Bilogora   Brod-Posavina   Dubrovnik-Neretva   Istria   Karlovac   Koprivnica-Križevci   Krapina-Zagorje   Lika-Senj   Međimurje   Osijek-Baranja   Požega-Slavonia   Primorje-Gorski Kotar   Šibenik-Knin   Sisak-Moslavina   Split-Dalmatia   Va...

 

Shoo (singer)

Zainichi Korean actress and singer (born 1981) In this Korean name, the family name is Yoo. ShooShoo in 2017BornShū Kunimitsu (邦光 洙) (1981-10-23) 23 October 1981 (age 42)Yokohama, JapanOther namesYoo Soo-youngEducationKorea Kent Foreign SchoolOccupationsActresssingerYears active1997–2018, 2022–presentSpouse Im Hyo-sung [ko] ​ ​(m. 2010)​Children3Musical careerGenresK-popInstrument(s)VocalsLabelsSMKorean nameHangul유수...

 

Sunshine Kitty

2019 studio album by Tove LoSunshine KittyStudio album by Tove LoReleased20 September 2019 (2019-09-20)RecordedJanuary–April 2019StudioMXM Studios(Stockholm, Sweden)MXM Studios(Los Angeles, US)House Mouse Studios(Stockholm)Jack & Coke Studios(Stockholm)Genre Electropop[1][2][3] synth-pop[4] Length40:27LanguageEnglishFrenchItalianPortugueseLabelIslandProducer Ludvig Söderberg The Struts Shellback Jax Jones Mark Ralph Ian Kirkpatric...

Nick Wright (footballer, born 1987)

English footballer For other people with the same name, see Nicholas Wright (disambiguation). Nick Wright Personal informationDate of birth (1987-11-25) 25 November 1987 (age 36)Place of birth Birmingham, EnglandPosition(s) StrikerYouth career Birmingham CitySenior career*Years Team Apps (Gls)2005–2007 Birmingham City 0 (0)2006 → Tamworth (loan) 1 (0)2006 → Bristol City (loan) 4 (0)2006 → Northampton Town (loan) 4 (0)2007 → Ashford Town (Kent) (loan) 10 (4)2007 Halesowen Town 8...

 

Frans Weisz

Frans WeiszFrans Weisz (1973)Lahir23 Juli 1938 (umur 85)Amsterdam, BelandaPekerjaanSutradaraTahun aktif1964–kini Frans Weisz (lahir 23 Juli 1938) adalah seorang sutradara asal Belanda. Ia menyutradarai 22 film sejak 1964. Film tahun 1975 buatannya Red Sien masuk dalam Festival Film Internasional Moskwa ke-9.[1] Film buatannya Havinck ditayangkan dalam sesi Un Certain Regard dari Festival Film Cannes 1988.[2] Film tahun 1993 buatannya The Betrayed masuk dalam Festi...

 

羅德島州

本條目存在以下問題，請協助改善本條目或在討論頁針對議題發表看法。 此條目需要擴充。 (2013年1月1日)请協助改善这篇條目，更進一步的信息可能會在討論頁或扩充请求中找到。请在擴充條目後將此模板移除。 此條目需要补充更多来源。 (2013年1月1日)请协助補充多方面可靠来源以改善这篇条目，无法查证的内容可能會因為异议提出而被移除。致使用者：请搜索一下条目的...

Повітряні сили Збройних сил України

Ця стаття потребує додаткових посилань на джерела для поліпшення її перевірності. Будь ласка, допоможіть удосконалити цю статтю, додавши посилання на надійні (авторитетні) джерела. Зверніться на сторінку обговорення за поясненнями та допоможіть виправити недоліки. Мат...

 

أقوى الرجال (فيلم)

أقوى الرجالملصق الفيلممعلومات عامةالصنف الفني جريمة، دراماتاريخ الصدور24 مارس 1993 (1993-03-24) (مصر)مدة العرض 104 دقيقةاللغة الأصلية العربيةالبلد  مصرالطاقمالمخرج أحمد السبعاويالكاتب عزيز نيسينالسيناريو والحوار بسيوني عثمانالبطولة نور الشريفسهير رمزيجمال إسماعي�...

 

List of intergovernmental organizations

A ministerial conference of the World Trade Organization, in the Palace of Nations (Geneva, Switzerland). The following is a list of the major existing intergovernmental organizations (IGOs). For a more complete listing, see the Yearbook of International Organizations,[1] which includes 25,000 international non-governmental organizations (INGOs), excluding for-profit enterprises, about 5,000 IGOs, and lists dormant and dead organizations as well as those in operation (figures as of t...

Fictional language

Constructed languages created for a fictional setting Not to be confused with Spurious languages. An example of Tolkien's Quenya, one of the languages of the elves, written in Tengwar with transliteration into a Latin-based alphabet. It translates to Ah! like gold fall the leaves in the wind, long years numberless as the wings of trees! Fictional languages are the subset of constructed languages (conlangs) that have been created as part of a fictional setting (e.g. for use in a book, movie, t...

 

المدة النيابية الثانية لمجلس النواب التونسي

هذه المقالة بحاجة لصندوق معلومات. فضلًا ساعد في تحسين هذه المقالة بإضافة صندوق معلومات مخصص إليها. يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (يوليو 2016) المدة ا...