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Uwe Schäfer

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

AutorSchäfer, Uwe

VerlagKIT Scientific Publishing, Karlsruhe

ISBN9783731502609

UmfangIV, 134 S.

Veröffentlicht
am:
03.12.2014

Erscheinungs-
jahr
2014

VerfügbarkeitAktiv

Downloads:

Für Zitate bitte die folgende URL verwenden:
http://dx.doi.org/10.5445/KSP/1000042944

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.