Joel H. Shapiro: A Fixed-Point Farrago

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Cover: 9783319802510 | A Fixed-Point Farrago | Joel H. Shapiro | Taschenbuch | Universitext

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Joel H. Shapiro is an adjunct professor of Mathematics and Statistics at Portland State University. He received his PhD from the University of Michigan.

Zusammenfassung

Acts as a perfect book for Graduate-level Fixed-Point Theory

Covers all major Fixed-Point theories in detail

Introduces Fixed-Point Theory and correlates it to several topics in Analysis

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	236
Reihe:	Universitext
Inhalt:	xiv 221 S. 8 s/w Illustr. 221 p. 8 illus.
ISBN-13:	9783319802510
ISBN-10:	3319802518
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Shapiro, Joel H.
Auflage:	Softcover reprint of the original 1st ed. 2016
Hersteller:	Springer International Publishing Universitext
Maße:	235 x 155 x 13 mm
Von/Mit:	Joel H. Shapiro
Erscheinungsdatum:	30.05.2018
Gewicht:	0,365 kg

preigu-id: 114225985