zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Iterative approximation of fixed points. 2nd revised and enlarged ed. (English) Zbl 1165.47047
Lecture Notes in Mathematics 1912. Berlin: Springer (ISBN 978-3-540-72233-5/hbk). xvi, 322 p. EUR 49.95/net; SFR 82.00; $ 74.00; £ 38.50 (2007).

There is a huge amount of existence results for fixed points, very often from a purely theoretical viewpoint, less often more application-oriented. There also exist some survey papers which describe the state of the art of some particular aspects, a prominent example being B. E. Rhoades’ comparison of various definitions of contractive-type maps [Trans. Am. Math. Soc. 226, 257–290 (1977; Zbl 0365.54023)]. However, less is known about specific methods for constructing or approximating fixed points effectively; the present book is intended to fill this gap.

A detailed description of the contents may be found in the review of the first edition (written by B. E. Rhoades) in [(2002; Zbl 1036.47037)]. Specialists in the field will find the list of more than 1500 references particularly useful; thus, this book may also serve as a guide to the literature.


MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47-00Reference works (operator theory)