# 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)
Fixed points in fuzzy metric spaces. (English) Zbl 0664.54032
{\it I. Kramosil} and {\it J. Michálek} [Kybernetika 11, 336-344 (1975; Zbl 0319.54002)] extended the concept of probabilistic metric spaces to fuzzy metric spaces. In this context, the author gives fuzzy versions of the Banach contraction principle and of the well-known fixed point theorem of {\it M. Edelstein} [J. Lond. Math. Soc. 37, 74-79 (1962; Zbl 0113.165)].
Reviewer: S.Sessa

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 54A40 Fuzzy topology
Full Text:
##### References:
 [1] Zi-Ke, Deng: Fuzzy pseudo metric spaces. J. math. Anal. appl. 86, 74-95 (1982) [2] Edelstein, M.: On fixed and periodic points under contractive mappings. J. London math. Soc. 37, 74-79 (1962) · Zbl 0113.16503 [3] Erceg, M. A.: Metric spaces in fuzzy set theory. J. math. Anal. appl. 69, 205-230 (1979) · Zbl 0409.54007 [4] Kaleva, O.; Seikkala, S.: On fuzzy metric spaces. Fuzzy sets and systems 12, 215-229 (1984) · Zbl 0558.54003 [5] Kramosil, J.; Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 334-336 (1975) · Zbl 0319.54002 [6] Kubiak, T.: A topological version of a coincidence theorem. (1981) [7] Ray, B. K.; Chatterjee, H.: Some results on fixed points in metric and Banach spaces. Bull. acad. Polon. math. 25, 1243-1247 (1977) · Zbl 0396.54039 [8] Schweizer, B.; Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 314-334 (1960) · Zbl 0091.29801