fixed point theorem in m-fuzzy metric spaces with property (e)

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1、AdvancesinFuzzyMathematics.ISSN0973-533XVol.1No.1(2006),pp.5565©ResearchIndiaPublicationshttp://www.ripublication.com/afm.htmFixedPointTheoreminM-FuzzyMetricSpaceswithproperty(E)S.Sedghi1andN.Shobe21DepartmentofMathematics,IslamicAzadUniversity-GhaemshahrBranch,IranE-mail:sedghi_gh@yahoo.c

2、om2DepartmentofMathematics,IslamicAzadUniversity-BabolBranch,IranE-mail:nabi_shobe@yahoo.comThecorrespondingauthor:sedghi_gh@yahoo.com(ShabanSedghi)AbstractInthispaper,acommonfixedpointtheoreminM-fuzzymetricspacesforproperty(E)isproved.AMSSubjectClassification:54E40,54E35,54H25.Keywords:M-Fu

3、zzycontractivemapping;CompleteM-fuzzymetricspace;Commonfixedpointtheorem.1.IntroductionandPreliminariesTheconceptoffuzzysetswasintroducedinitiallybyZadeh[15]in1965.Sincethen,tousethisconceptintopologyandanalysismanyauthorshaveexpansivelydevelopedthetheoryoffuzzysetsandapplication.GeorgeandV

4、eeramani[6]andKramosilandMichalek[8]haveintroducedtheconceptoffuzzytopologicalspacesinducedbyfuzzymetricwhichhaveveryimportantapplicationsinquantumparticlephysicsparticularlyinconnectionswithbothstringandE-infinitytheorywhichweregivenandstudiedbyElNaschie[25,14].Manyauthors[7,10,11,13]havep

5、rovedfixedpointtheoreminfuzzy(probabilistic)metricspaces.Oneshouldthereexistsaspacebetweenspaces.AndonesuchgeneralizationisgeneralizedmetricspaceorD-metricspaceinitiatedbyDhage[1]in1992.Heprovedsomeresultsonfixedpointsforaself-mapsatisfyingacontractionforcompleteandboundedD-metricspaces.Rhoa

6、des[9]generalizedDhagescontractiveconditionbyincreasingthenumberoffactorsandprovedtheexistenceofuniquefixedpointofaself-mapinD-metricspace.Recently,motivatedbytheconcept56SedghiandShobeofcompatibilityformetricspace,SinghandSharma[12]introducedtheconceptofD-compatibilityofmapsinD-metricspace

7、andprovedsomefixedpointtheoremsusingacontractivecondition.Inwhatfollows(X,D)willdenoteaD-metricspace,Nthesetofallnaturalnumbers,andR+thesetofallpositiverealnumbers.Definition1.1.LetXbeanonemptyset.Ageneralizedmetric(orD-metric)onXisafunction:D:X3−→R+thatsatisfies