Fixed Point Theory [Hardcover]

Andrzej Granas (Author), James Dugundji (Author)

Book Description

ISBN-10: 0387001735 | ISBN-13: 978-0387001739 | Publication Date: June 26, 2003 | Edition: 1

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS

Editorial Reviews

Review

From the reviews: "Granas-Dugundji’s book is an encyclopedic survey of the classical fixed point theory of continuous maps (the work of Poincaré, Brouwer, Lefschetz-Hopf, Leray-Schauder) and all its various modern extensions.  This is certainly the most learned book ever likely to be published on this subject." -Felix Browder, Rutgers University "The theory of Fixed Points is one of the most powerful tools of modern mathematics.  Not only is it used on a daily basis in pure and applied mathematics, but it also serves as a bridge between Analysis and Topology, and provides a very fruitful area of interaction between the two.  This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications" -Haim Brézis, Rutgers University "This is the most comprehensive, well-written and complete book on fixed point theory to date. The book studies just about every aspect of fixed point theory … . The book carries an extensive literature on the subject and many examples. Many of the interesting results, given as exercises, constitute an extension of the theory established in the main text. … I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." (A.G. Kartsatos, Mathematical Reviews, 2004d) "Thousands of papers have been published in fixed point theory and its applications … . The book of Granas and Dugundji is a new and major contribution to this purpose. … The main text is self-contained, the necessary background material being collected in an appendix … . I can assert this monograph represents an exceptional event and I am sure it will become a reference work in the field. … this book will be extremely valuable to anyone involved in fixed point theory … ." (R. Precup, ZAA-Zeitschrift für Analysis und ihre Anwendungen, Vol. 23 (2), 2004) "The new edition of Granas and Dugundji’s book is, in my opinion, the most important and complete survey in the last years on fixed point theory … . The main text is self-contained … . New and interesting results and applications can be found all over the book. The style is alert and pleasant. The technical presentation of the book is exceptional. … it will be a very useful work for anyone … involved in fixed point theory in particular and nonlinear analysis in general." (Adrian Petrusel, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLIX (1), 2004) "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." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003) "Really, this book is an up-to-date and carefully worked out unified account of (not only) classical results in fixed point theory … . 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. … The rich bibliography comprises almost 50 pages. The book is useful to all mathematicians who deal with fixed points. It will become an obligatory volume for every serious mathematical library." (Peter Zabreiko, Zentralblatt MATH, Vol. 1025, 2003) "This monograph provides an immense text … on classical topics in fixed point theory that lie on the borderline of topology and nonlinear functional analysis. … The book is well understandable and requires only a basic knowledge of topology and functional analysis … . It can be warmly recommended to a broad spectrum of readers – to graduate students, experts and everybody who wishes to become acquainted with the basic elements and deeper properties of this part of functional analysis." (EMS Newsletter, March, 2005)

From the Back Cover

"Granas-Dugundji's book is an encyclopedic survey of the classical fixed point theory of continuous mappings (the work of Poincaré, Brouwer, Lefschetz-Hopf, Leray-Schauder) and all its various modern extensions. This is certainly the most learned book ever likely to be published on this subject." -Felix Browder, Rutgers University "The theory of Fixed Points is one of the most powerful tools of modern mathematics. Not only is it used on a daily basis in pure and applied mathematics, but it also serves as a bridge between Analysis and Topology, and provides a very fruitful area of interaction between the two. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications." -Haïm Brézis, Université Pierre et Marie Curie "In this monograph, no effort has been spared, even to the smallest detail, be it mathematical, historical or bibliographical. In particular, the necessary background materials are generously provided for non-specialists. In fact, the book could even serve as an introduction to algebraic topology among others. It is certain that the book will be a standard work on Fixed Point Theory for many years to come." -Isaac Namioka, University of Washington 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. Andrzej Granas studied in Warsaw and then Moscow, where he earned his Ph.D. in 1958 under Lazar Lusternik. Since 1958, he has held various research and teaching posts in Poland, USA, Canada and elsewhere. During the Spring of 1970, he occupied a special chair at the Collège de France. In the early nineties, Dr. Granas founded and edited the journal Topological Methods of Nonlinear Analysis, and since 1992, he has served on the editorial board of the Zentralblatt. He is an Honorary Member of the Gdansk Scientific Society. The first part of this book is based on "Fixed Point Theory I" which was published by PWN, Warsaw in 1982. The second part follows the outline conceived by Andrzej Granas and the late James Dugundji.  

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Product Details

• Hardcover: 552 pages
• Publisher: Springer; 1 edition (June 26, 2003)
• Language: English
• ISBN-10: 0387001735
• ISBN-13: 978-0387001739
• Product Dimensions: 8.8 x 6.2 x 1.9 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #881,202 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 12 people found the following review helpful:

5.0 out of 5 stars A definitive work marred by cheap production techniques, June 16, 2008

By 

Christopher Grant (Salem, UT USA) - See all my reviews
(REAL NAME)   

This review is from: Fixed Point Theory (Hardcover)

I've been examining this book carefully for the last several weeks for possible use in a nonlinear analysis course I am constructing at Brigham Young University. All the positive things that the professional reviews say are true: this is really a remarkable work!

But here's the problem: If you order this book now, you will probably receive a low-grade digital reprint, as I did when my copy arrived from Amazon this afternoon. Gone is the sturdy sewn binding of the original printing, the graphics now look like they were produced on a 1980s vintage dot matrix printer, and the digital reprinting process makes it even difficult to tell bold from regular type. Advanced mathematics uses symbols with fine detail; the more difficult that detail is to discern, the more difficult the content is to absorb. To present the fine work of Dugundji and Granas in this inferior format is a travesty.

Publishers freely acknowledge the difference between hardcover and softcover books in their advertising and pricing; why won't they do the same when it comes to the difference between an original printing and a digital reprint?

I sent my copy back for a refund, and I'll refrain from purchasing any more math texts that have been given this "digital printing" treatment in the future. To the extent that I am aware of their status, I will also henceforth refrain from adopting such texts for courses I teach. I'm probably tilting at windmills, but these cheap knockoffs are apparently becoming more and more common, and if there's even a slight chance of getting publishers to think twice about cutting corners like this, it will be worth it.

[December 2009 Update: The author has contacted me about my previous 2-star rating hurting his sales, so I have changed the rating to 5-stars, even though "I don't like it" still captures my feelings about this book as Springer is currently producing it. I will not buy it in its current state.]