The Resource Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)
Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)
Resource Information
The item Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This book provides a primary resource in basic fixedpoint 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 fixedpoint 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 fixedpoint theorem. It elaborates Manka’s proof of the fixedpoint property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixedpoint 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.
 Language
 eng
 Extent
 1 online resource (XIII, 302 pages)
 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
 Isbn
 9789811331589
 Label
 Elementary Fixed Point Theorems
 Title
 Elementary Fixed Point Theorems
 Statement of responsibility
 by P.V. Subrahmanyam
 Language
 eng
 Summary
 This book provides a primary resource in basic fixedpoint 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 fixedpoint 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 fixedpoint theorem. It elaborates Manka’s proof of the fixedpoint property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixedpoint 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.
 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)
 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
 9789811331589
 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, noncommercial 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)
 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
 9789811331589
 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, noncommercial 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/ElementaryFixedPointTheoremsbyP.V./dljPYVUm5KU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/ElementaryFixedPointTheoremsbyP.V./dljPYVUm5KU/">Elementary Fixed Point Theorems, by P.V. Subrahmanyam, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>