A Fixed-Point Farrago
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※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 1st ed. 2016 Series: Universitext Author: Shapiro, Joel H. Publisher: Springer ISBN: 9783319279763 Cover: HARDCOVER Date: 2016年05月 DESCRIPTION 最も良く知られる不動点定理の解析に関するテーマとの相互関係を中心に紹介。本書を読み進めるうちに学部生の基礎レベルから高度な大学院生レベルまで徐々にレベルを上げて解説。付録では必修の題材をいくつか紹介(あるいは補充)し、演習問題も収載することで、自己充足型の書籍として活用できる。特に自習用として、また、不動点理論の学部課程のサポート教材として役立つ一冊である。 本書の構成: 第1部:Banachの縮小写像の定理やBrouwerの不動点定理の紹介と興味深い応用例。 第2部:Brouwerの定理とこれをJohn Nashの研究に応用した事例を紹介。 第3部:Brouwer定理の無限次元空間への応用。 第4部:アフィン写像のfamiliesに対する不動点をめぐるMarkov、角谷およびRyll Nardzewskiの研究について。 This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume's ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer's theorem and its application to John Nash's work; the third applies Brouwer's theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll Nardzewski surrounding fixed points for families of affine maps. TABLE OF CONTENTS This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory.The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll-Nardzewski surrounding fixed points for families of affine maps.
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