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The Resource A Fixed-Point Farrago, by Joel H. Shapiro, (electronic resource)

A Fixed-Point Farrago, by Joel H. Shapiro, (electronic resource)

Creator
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. 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--
Language
eng
Work
Publication
Extent
1 online resource (xiv, 221 pages)
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
Isbn
9783319279787
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-27978-7
Instance
Label
A Fixed-Point Farrago
Title
A Fixed-Point Farrago
Statement of responsibility
by Joel H. Shapiro
Creator
Subject
Language
eng
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. 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--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Shapiro, Joel H
Image bit depth
0
Literary form
non fiction
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematical analysis
  • Analysis (Mathematics)
  • Numerical analysis
Label
A Fixed-Point Farrago, by Joel H. Shapiro, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-27978-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
978-3-319-27978-7
Dimensions
unknown
Extent
1 online resource (xiv, 221 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319279787
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-27978-7
Other physical details
8 illustrations.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)951214711
Label
A Fixed-Point Farrago, by Joel H. Shapiro, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-27978-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
978-3-319-27978-7
Dimensions
unknown
Extent
1 online resource (xiv, 221 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319279787
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-27978-7
Other physical details
8 illustrations.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)951214711

Subject

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