zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Contraction mappings and extensions. (English) Zbl 1019.54001
Kirk, William A. (ed.) et al., Handbook of metric fixed point theory. Dordrecht: Kluwer Academic Publishers. 1-34 (2001).
The paper presents the basic results on generalized contractions. It covers the following topics: contraction principle, extensions of contraction principle, Brondsted’s partial order on metric spaces and fixed points, setvalued contractions, probabilistic metrics and fuzzy sets, converses to the contraction principle, topological extensions of the contraction principle, structure of the fixed point set of a multivalued contraction and random fixed point theory. The bibliography represents an excellent starting point in metrical fixed point theory. For the entire collection see [Zbl 0970.54001].

54-02Research monographs (general topology)
54H25Fixed-point and coincidence theorems in topological spaces
54E50Complete metric spaces
54E40Special maps on metric spaces
54E70Probabilistic metric spaces