Li Yaohua
Abstract
A new proof of the Leray-Schauder fixed point theorem is established in this paper.By the set valued version of pasting lemma and the Kakutani fixed point theorem,we prove the Leray-Schauder fixed point theorem.The equivlence between the Brouwer fixed point theorem and the Leray-Schauder fixed point theorem is established.
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A new proof of the Leray-Schauder fixed point theorem is established in this paper.By the set valued version of pasting lemma and the Kakutani fixed point theorem,we prove the Leray-Schauder fixed point theorem.The equivlence between the Brouwer fixed point theorem and the Leray-Schauder fixed point theorem is established.
Key concepts: Fixed-point theorem, Schauder fixed point theorem, Mathematics, Kakutani fixed-point theorem, Brouwer fixed-point theorem, Picard–Lindelöf theorem, Fixed-point property, Lemma (botany)