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Fixed point theory

Author: Andrzej Granas; James Dugundji
Publisher: New York : Springer, ©2003.
Series: Springer monographs in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This monograph gives a carefully worked-out account of the most basic principles and applications of the theory of fixed points. Until now, a treatment of many of the discussed topics has been unavailable in book form. The presentation is self-contained and is accessible to a broad spectrum of readers. The main text is complemented by numerous exercises, detailed comments, and a comprehensive bibliography."--Jacket.
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Andrzej Granas; James Dugundji
ISBN: 0387001735 9780387001739
OCLC Number: 51046891
Description: xv, 690 pages : illustrations ; 25 cm.
Contents: I. Elementary Fixed Point Theorems --
1. Results Based on Completeness --
2. Order-Theoretic Results --
3. Results Based on Convexity --
4. Further Results and Applications --
II. Theorem of Borsuk and Topological Transversality --
5. Theorems of Brouwer and Borsuk --
6. Fixed Points for Compact Maps in Normed Linear Spaces --
7. Further Results and Applications --
III. Homology and Fixed Points --
8. Simplicial Homology --
9. The Lefschetz-Hopf Theorem and Brouwer Degree --
IV. Leray-Schauder Degree and Fixed Point Index --
10. Topological Degree in R [subscript n] --
11. Absolute Neighborhood Retracts --
12. Fixed Point Index in ANRs --
13. Further Results and Applications --
V. The Lefschetz-Hopf Theory --
14. Singular Homology --
15. Lefschetz Theory for Maps of ANRs --
16. The Hopf Index Theorem --
17. Further Results and Applications --
VI. Selected Topics --
18. Finite-Codimensional Cech Cohomology --
19. Vietoris Fractions and Coincidence Theory --
20. Further Results and Supplements.
Series Title: Springer monographs in mathematics.
Responsibility: Andrzej Granas, James Dugundji.
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Abstract:

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This title contains a presentation of the major results, together with a set of historical notes and a bibliography  Read more...

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From the reviews:"Granas-Dugundji's book is an encyclopedic survey of the classical fixed point theory of continuous maps (the work of Poincare, Brouwer, Lefschetz-Hopf, Leray-Schauder) and all its Read more...

 
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