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

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 natura...

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1. Verfasser:	Schäfer, Uwe
Format:	Buch
Sprache:	eng
Schlagworte:	Anwendungen Banach spaces Banachräume Book Industry Communication Brouwer Fixpunkt Mathematics & science QA1-939 SchauderFixed points verification methods
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creator	Schäfer, Uwe
description	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.
doi_str_mv	10.5445/KSP/1000042944
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subjects	Anwendungen Banach spaces Banachräume Book Industry Communication Brouwer Fixpunkt Mathematics & science QA1-939 SchauderFixed points verification methods
title	From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications
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