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)
A class of contractions in fuzzy metric spaces. (English) Zbl 1189.54035
Summary: Using the notion of geometrically convergent t-norms, a fixed point theorem in fuzzy metric spaces in the sense of Kramosil and Michalek for a class of contractions, larger than the class of (ε,λ)-contraction mappings, has been proved.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E70Probabilistic metric spaces
References:
[1]Deng, Zi-Ke: Fuzzy pseudo-metric spaces, J. math. Anal. appl. 86, 74-95 (1982) · Zbl 0501.54003 · doi:10.1016/0022-247X(82)90255-4
[2]George, A.; Veeramani, P.: On some results in fuzzy metric spaces, Fuzzy sets and systems 64, 35-39 (1994) · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[3]Gregori, V.; Sapena, A.: On fixed point theorems in fuzzy metric spaces, Fuzzy sets and systems 125, 245-252 (2002) · Zbl 0995.54046 · doi:10.1016/S0165-0114(00)00088-9
[4]Hadžić, O.; Budinčević, M.: A fixed point theorem in PM spaces, Colloq. math. Soc. J. Bolyai 23, 569-579 (1978)
[5]Hadžić, O.; Pap, E.: Fixed point theory in probabilistic metric spaces, (2001)
[6]Hadžić, O.; Pap, E.; Budinčević, M.: Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetika 38, No. 3, 363-381 (2002)
[7]Hadžić, O.; Pap, E.; Budinčević, M.: A generalization of tardiff’s fixed point theorem in probabilistic metric spaces and applications to random equations, Fuzzy sets and systems 156, 124-134 (2005) · Zbl 1086.54018 · doi:10.1016/j.fss.2005.04.007
[8]Hadžić, O.; Pap, E.: Fixed point theorems for single-valued and multivalued mappings in probabilistic metric spaces, Atti sem. Mat. fiz. Modena Li, 377-395 (2003)
[9]Hadžić, O.; Pap, E.: New classes of probabilistic contractions and applications to random operators, Fixed point theory and application 4, 97-119 (2003) · Zbl 1069.54026
[10]Kaleva, O.; Seikkala, S.: On fuzzy metric spaces, Fuzzy sets and systems 12, 215-229 (1984) · Zbl 0558.54003 · doi:10.1016/0165-0114(84)90069-1
[11]Kramosil, I.; Michalek, J.: Fuzzy metrics and statistical metric spaces, Kybernetika 11, 336-344 (1975) · Zbl 0319.54002
[12]Miheţ, D.: A class of sehgal’s contractions in probabilistic metric spaces, An. univ. Vest timisoara ser. Mat. informatica 37, 105-110 (1999) · Zbl 0997.54048
[13]Miheţ, D.: A Banach contraction theorem in fuzzy metric spaces, Fuzzy sets and systems 144, 431-439 (2004) · Zbl 1052.54010 · doi:10.1016/S0165-0114(03)00305-1
[14]Miheţ, D.: On the existence and the uniqueness of fixed points of sehgal contractions, Fuzzy sets and systems 156, 135-141 (2005) · Zbl 1082.54022 · doi:10.1016/j.fss.2005.05.024
[15]Miheţ, D.: Multivalued generalizations of probabilistic contractions, J. math. Anal. appl. 304, 464-472 (2005) · Zbl 1072.47066 · doi:10.1016/j.jmaa.2004.09.034
[16]Miheţ, D.: A note on a paper of hadžić and pap, Fixed point theory and applications 7, 127-133 (2007)
[17]V. Radu, Some Fixed Point Theorems in PM Spaces, in: Lectures Notes in Mathematics, Vol. 1233, 1987, pp. 125 – 133.
[18]V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, in: The 8-th Internat. Conf. on Applied Mathematics and Computer Science, Cluj-Napoca, 2002, Automat. Comput. Appl. Math. 11 (2002) 125 – 131.
[19]Schweizer, B.; Sklar, A.: Probabilistic metric spaces, (1983)
[20]Schweizer, B.; Sherwood, H.; Tardif, R. M.: Contractions on PM-spaces: examples and counterexamples, Stochastica 12, No. 1, 5-17 (1988) · Zbl 0689.60019
[21]S. Sedghi, T. Žikić-Došenović, N. Shobe, Common fixed point theorems in Menger probabilistic quasimetric spaces, in: Fixed Point Theory and Applications, Vol. 2009, 2009, Article ID 546273, doi:10.1155/2009/546273. · Zbl 1171.54035 · doi:10.1155/2009/546273
[22]Sehgal, V. M.; Bharucha-Reid, A. T.: Fixed points of contraction mappings on PM-spaces, Math. syst. Theory 6, 97-100 (1972) · Zbl 0244.60004 · doi:10.1007/BF01706080
[23]Sherwood, H.: Complete probabilistic metric spaces, Wahr. verw. Geb. 20, 117-128 (1971) · Zbl 0212.19304 · doi:10.1007/BF00536289
[24]P. Tirado, Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets, in: VII Iberoamerican Conf. on Topology and its Applications, Valencia, Spain, 25 – 28 June 2008.
[25]Žikić, T.: On fixed point theorems of gregori and sapena, Fuzzy sets and systems 144, No. 3, 421-429 (2004) · Zbl 1052.54006 · doi:10.1016/S0165-0114(03)00179-9