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

• Tác giả: Uwe Schäfer
• Ngôn ngữ: eng
• ISBN-13: 978-3731502609
• ISBN: KSP/1000042944
• Ký hiệu phân loại: 510 Mathematics
• Thông tin xuất bản: Karlsruhe : KIT Scientific Publishing, 2014
• Mô tả vật lý: 1 electronic resource (IV, 134 p. p.)
• Bộ sưu tập: Tài liệu truy cập mở
• ID: 228893

Tóm tắt

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.