Nonlinear Functional Analysis and its Applications: Part 1: Fixed-Point Theorems (Zeidler, Eberhard//Nonlinear Functional Analysis and Its Applications) (Pt. 1) [Hardcover]

Eberhard Zeidler (Author), P.R. Wadsack (Translator)

Book Description

Publication Date: December 13, 1985 | ISBN-10: 0387909141 | ISBN-13: 978-0387909141

From the reviews: "...has a flowing, coherent form and contains nice comments, overviews, and perspectives on the strategy and implementations of the considered procedures, and is concluded with complementary problems. Moreover, at the end of each volume there is a comprehensive and up-to-date bibliography. The work is clearly written and organized so that each chapter can be independently approached." (Zentralblatt für Mathematik und ihre Grenzgebiete) "The book is in fact dedicated to a large area of applications. Mathematicians, engineers, and natural scientists will find many interesting results." (Acta Applicandae Mathematicae)

Editorial Reviews

Language Notes

Text: English, German (translation)

Product Details

• Hardcover: 932 pages
• Publisher: Springer (December 13, 1985)
• Language: English
• ISBN-10: 0387909141
• ISBN-13: 978-0387909141
• Product Dimensions: 9.3 x 6.5 x 2 inches
• Shipping Weight: 3.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #376,565 in Books (See Top 100 in Books)

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7 of 7 people found the following review helpful:

5.0 out of 5 stars Incredible Work, September 13, 2000

By 

Kevin R. Vixie (Los Alamos, NM) - See all my reviews
(REAL NAME)   

This review is from: Nonlinear Functional Analysis and its Applications: Part 1: Fixed-Point Theorems (Zeidler, Eberhard//Nonlinear Functional Analysis and Its Applications) (Pt. 1) (Hardcover)

This is the first book in an incredible five volume work on Nonlinear Functional analysis and it's applications. The volumes -- i) Fixed Point Theorems, iia) Linear Monotone Operators, iib) Nonlinear Montone Operators, iii) Variational Methods and Optimization, iv) Applications to Mathematical Physics -- are together over 3700 pages in length!!!

The 8 indices (I use the term broadly) of volume I are -- 1) Symbols, 2) Theorems, 3) Important Definitions, 4) Schematic Overviews, 5) General References to the Literature, 6) List of Important Principles, 7) Contents of the other Volumes, 8) The Index -- just to give an idea of the detail and care with which these volumes were prepared.

The Appendices found at the backs of I, IIb and III are themselves an impresive collection of facts from analysis and linear functional analysis. (In fact when I want a quick reminder of some fact or am curious about extensions of some concept, I often go here first or in conjunction with a handful of other books most notably Evans and Gariepy's "Measure theory and ...", Folland's "Real Analysis" and Conway's "A Course in Functional Analysis".)

The problem collection is an incredible work in itself with references to papers in which the problems are studied in detail. The problems themselves are mini-expositions in extensions and side explorations not found in the main text.

Another beautiful feature is the very large collection of pertinent and often quite entertaining quotes that appear throughout.

The text reads very smoothly and speaks very well of the translation efforts of P. Wadsack, L. Boron, and J. Quandt. There are minor mistakes that I have never found disturbing. In fact the mistakes keep me engaged, though I imagine they might cause some difficulty for someone with a weak background in analysis. Nevertheless, I recommend these books to anyone seriously interested in nonlinear analysis. I recommend them not only because of their comprehensiveness, not only because they are fun to work through or even just read, but also because they include an incredible collection of annotated references.

The only serious drawback to these volumes are their price and the difficulty that one sometimes has obtaining them. But to be fair I should add that I think the books are worth the price since in fact I have the whole set.

The first volume on fixed point theory is large (909 pages). This alone gives an indication of the ground taken in by fixed point theory in nonlinear analysis. The three "main" fixed point theorems -- the Banach, Schauder, and Bourbaki-Kneser fixed point theorems -- occupy, together with their extensive applications, the first 516 pages of the book. The last 393 pages are an exposition of mapping degree and fixed point index theory (and their applications). The author makes great efforts to keep the presentation of degree and index theory as simple as possible -- but not too simple!

I recommend the volume.

2 of 2 people found the following review helpful:

5.0 out of 5 stars The most comprehensive book on fixed-point theorems, December 21, 1996

By A Customer

This review is from: Nonlinear Functional Analysis and its Applications: Part 1: Fixed-Point Theorems (Zeidler, Eberhard//Nonlinear Functional Analysis and Its Applications) (Pt. 1) (Hardcover)

This is an excellent book on fixed theorems both for beguiners and experts alike.

The only complaint I have about the book is that It is impossible to buy. I have been trying to buy a copy since 1991!
I have called the publisher in Germany several times, but always the same answer: out of stock, will be reprinted soon.

Can any one help me get hold of a copy (new or used)?

my e-mail is [e-mail]