TY - BOOK ID - 100313594 TI - From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications PY - 2014 SN - 1000042944 3731502607 PB - KIT Scientific Publishing DB - UniCat KW - Banachräume KW - Brouwer KW - SchauderFixed points KW - Fixpunkt KW - Anwendungen KW - Banach spaces KW - verification methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:100313594 AB - 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. ER -