Coverart for item
The Resource Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)

Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)

Label
Elementary Fixed Point Theorems
Title
Elementary Fixed Point Theorems
Statement of responsibility
by P.V. Subrahmanyam
Creator
Subject
Language
eng
Summary
This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky’s theorem on periodic points, Thron’s results on the convergence of certain real iterates, Shield’s common fixed theorem for a commuting family of analytic functions and Bergweiler’s existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski’s theorem by Merrifield and Stein and Abian’s proof of the equivalence of Bourbaki–Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward’s theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka’s proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy–Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder–Gohde–Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Subrahmanyam, PV
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Springer eBooks
  • Springer eBooks.
  • Forum for Interdisciplinary Mathematics,
http://library.link/vocab/subjectName
Global analysis (Mathematics)
Label
Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-981-13-3158-9
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Chapter 1. Prerequisites -- Chapter 2. Fixed Points of Some Real and Complex Functions -- Chapter 3. Fixed Points and Order -- Chapter 4. Partially Ordered Topological Spaces and Fixed Points -- Chapter 5. Contraction Principle -- Chapter 6. Applications of the Contraction Principle -- Chapter 7. Caristi’s fixed point theorem -- Chapter 8. Contractive and Nonexpansive Mappings -- Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings -- Chapter 10. Brouwer’s Fixed Point Theorem -- Chapter 11. Schauder’s Fixed Point Theorem and Allied Theorems -- Chapter 12. Basic Analytic Degree Theory af a Mapping
Control code
978-981-13-3158-9
Dimensions
unknown
Extent
1 online resource (XIII, 302 pages)
Form of item
  • online
  • 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
9789811331589
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
5 illustrations
Specific material designation
remote
System control number
(OCoLC)1083095872
Label
Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-981-13-3158-9
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Chapter 1. Prerequisites -- Chapter 2. Fixed Points of Some Real and Complex Functions -- Chapter 3. Fixed Points and Order -- Chapter 4. Partially Ordered Topological Spaces and Fixed Points -- Chapter 5. Contraction Principle -- Chapter 6. Applications of the Contraction Principle -- Chapter 7. Caristi’s fixed point theorem -- Chapter 8. Contractive and Nonexpansive Mappings -- Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings -- Chapter 10. Brouwer’s Fixed Point Theorem -- Chapter 11. Schauder’s Fixed Point Theorem and Allied Theorems -- Chapter 12. Basic Analytic Degree Theory af a Mapping
Control code
978-981-13-3158-9
Dimensions
unknown
Extent
1 online resource (XIII, 302 pages)
Form of item
  • online
  • 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
9789811331589
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
5 illustrations
Specific material designation
remote
System control number
(OCoLC)1083095872

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