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

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The book explores the proof of Brouwer's fixed point theorem through Sperner's lemma and emphasizes practical applications rather than alternative proofs. It introduces Schauder's fixed point theorem, which extends Brouwer's theorem to infinite-dimensional spaces. Additionally, Tarski's fixed point theorem is examined, particularly its relevance to differential equations in Banach spaces, showcasing the theorem's broader implications in mathematical analysis and topology.