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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| Format: | eBook |
| Language: | English |
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KIT Scientific Publishing
2014
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| Collection: | Directory of Open Access Books - Collection details see MPG.ReNa |
| Summary: | 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. |
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| Item Description: | Creative Commons (cc), https://creativecommons.org/licenses/by-sa/4.0/ |
| Physical Description: | 1 electronic resource (IV, 134 p. p.) |
| ISBN: | 9783731502609 1000042944 |