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DOI: 10.5445/KSP/1000042944
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From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications

Schäfer, Uwe

Abstract:
Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Buch
Jahr 2014
Sprache Englisch
Identifikator ISBN: 978-3-7315-0260-9
URN: urn:nbn:de:0072-429447
KITopen-ID: 1000042944
Verlag KIT Scientific Publishing, Karlsruhe
Umfang IV, 134 S.
Schlagworte Fixpunkt, Anwendungen, Banachräume, Brouwer, Schauder Fixed points, verification methods, Banach spaces
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