Elementary Fixed Point Theorems

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 fixe...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Subrahmanyam, P.V (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Singapore : Springer Singapore : Imprint: Springer, 2018.
Έκδοση:1st ed. 2018.
Σειρά:Forum for Interdisciplinary Mathematics,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03984nam a2200457 4500
001 978-981-13-3158-9
003 DE-He213
005 20191220125600.0
007 cr nn 008mamaa
008 190110s2018 si | s |||| 0|eng d
020 |a 9789811331589  |9 978-981-13-3158-9 
024 7 |a 10.1007/978-981-13-3158-9  |2 doi 
040 |d GrThAP 
050 4 |a QA299.6-433 
072 7 |a PBK  |2 bicssc 
072 7 |a MAT034000  |2 bisacsh 
072 7 |a PBK  |2 thema 
082 0 4 |a 515  |2 23 
100 1 |a Subrahmanyam, P.V.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Elementary Fixed Point Theorems  |h [electronic resource] /  |c by P.V. Subrahmanyam. 
250 |a 1st ed. 2018. 
264 1 |a Singapore :  |b Springer Singapore :  |b Imprint: Springer,  |c 2018. 
300 |a XIII, 302 p. 5 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Forum for Interdisciplinary Mathematics,  |x 2364-6748 
505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematical analysis. 
650 0 |a Analysis (Mathematics). 
650 1 4 |a Analysis.  |0 http://scigraph.springernature.com/things/product-market-codes/M12007 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9789811331572 
776 0 8 |i Printed edition:  |z 9789811331596 
830 0 |a Forum for Interdisciplinary Mathematics,  |x 2364-6748 
856 4 0 |u https://doi.org/10.1007/978-981-13-3158-9  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)