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A fixed-point Farrago

Author: Joel H Shapiro
Publisher: Switzerland : Springer, [2016] ©2016
Series: Universitext
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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.
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Document Type: Book
All Authors / Contributors: Joel H Shapiro
ISBN: 9783319279763 3319279769
OCLC Number: 956532234
Description: xiv, 221 pages : illustrations ; 24 cm
Contents: 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.
Series Title: Universitext
Responsibility: Joel H. Shapiro.

Abstract:

This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis.  Read more...

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"This is a well-written and essentially self-contained survey on several applications of fixed-point theory. ... The book makes easy reading because the proofs are remarkably well structured. They Read more...

 
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