大葉大學圖書館 |

A fixed-point Farrago[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.7248
書名/作者:	A fixed-point Farrago/ by Joel H. Shapiro.
作者:	Shapiro, Joel H.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiv, 221 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Fixed point theory.
標題:	Mathematics.
標題:	Analysis.
標題:	Numerical Analysis.
ISBN:	9783319279787
ISBN:	9783319279763
內容註:	1. From Newton to Google -- 2. Brouwer in Dimension Two -- 3. Contraction Mappings -- 4. Brouwer in Higher Dimensions -- 5. Nash Equilibrium -- 6. Nash's "one-page proof" -- 7. The Schauder Fixed-Point Theorem -- 8. The Invariant Subspace Problem -- 9. The Markov-Kakutani Theorem -- 10. The Meaning of Means -- 11. Paradoxical Decompositions -- 12. Fixed Points for Non-commuting Map Families -- 13. Beyond Markov-Kakutani -- A. Advanced Calculus -- B. Compact Metric Spaces -- C. Convex Sets and Normed Spaces -- D. Euclidean Isometries -- E. A Little Group Theory, a Little Set Theory -- References -- Index -- List of Symbols.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-27978-7

A fixed-point Farrago[electronic resource] /
Shapiro, Joel H.

A fixed-point Farrago[electronic resource] /by Joel H. Shapiro. - Cham :Springer International Publishing :2016. - xiv, 221 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

1. From Newton to Google -- 2. Brouwer in Dimension Two -- 3. Contraction Mappings -- 4. Brouwer in Higher Dimensions -- 5. Nash Equilibrium -- 6. Nash's "one-page proof" -- 7. The Schauder Fixed-Point Theorem -- 8. The Invariant Subspace Problem -- 9. The Markov-Kakutani Theorem -- 10. The Meaning of Means -- 11. Paradoxical Decompositions -- 12. Fixed Points for Non-commuting Map Families -- 13. Beyond Markov-Kakutani -- A. Advanced Calculus -- B. Compact Metric Spaces -- C. Convex Sets and Normed Spaces -- D. Euclidean Isometries -- E. A Little Group Theory, a Little Set Theory -- References -- Index -- List of Symbols.

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.

ISBN: 9783319279787

Standard No.: 10.1007/978-3-319-27978-7doiSubjects--Topical Terms:

556234
Fixed point theory.

LC Class. No.: QA329.9

Dewey Class. No.: 515.7248

A fixed-point Farrago[electronic resource] /
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520 $a 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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