Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
FASCICULI
MATHEMATICI
Nr39
2008
MujahidAbbas
COMMONFIXEDPOINTRESULTSWITH
APPLICATIONSINCONVEXMETRICSPACE
Abstract.Sufficientconditionsfortheexistenceofacommon
fixedpointforuniformlyCq−commutingmappingssatisfyinga
generalizedcontractiveconditionsintheframeworkofaconvex
metricspaceareobtained.Asanapplication,relatedresultson
bestapproximationarederived.Ourresultsgeneralizevarious
knownresultsintheliterature.
Keywords:Convexmetricspace,commonfixedpoint,uni-
formlyCq−commutingmapping,asymptoticallyS−nonexpan-
sivemapping,bestapproximation.
AMSMathematicsSubjectClassification:47H09,47H10,47H19,
54H25.
1.Introductionandpreliminaries
Metricfixedpointtheoryisabranchoffixedpointtheorywhichfinds
itsprimaryapplicationsinfunctionalanalysis.Theinterplaybetweenthe
geometryofBanachspacesandfixedpointtheoryhasbeenverystrongand
fruitful.Inparticular,geometricconditionsonmappingsand/orunderlying
spacesplayacrucialroleinmetricfixedpointproblems.Althoughithas
apurelymetricflavor,itisalsoamajorbranchofnonlinearfunctional
analysiswithclosetiestoBanachspacegeometry,seeforexample[10]and
referencesmentionedtherein.Severalresultsconcerningtheexistenceand
approximationofafixedpointofamappingrelyonconvexityhypotheses
andgeometricpropertiesoftheBanachspaces.Takahashi[21]introduced
thenotionofaconvexityonmetricspaces.Afterwards,BegandAbbas([4],
[5]),Ciric[8],Ding[9],Guay,SinghandWhitfield[11]andotherauthors
havestudiedfixedpointtheoremsinconvexmetricspaces(seealso[6],
[19]).Ontheotherhand,Shahzad[18]introducedaclassofnoncommuting
mappingscalledR−subweaklycommutingmappings,andappliedittoS−
nonexpansivemappingsinnormedspaces.Inthispaper,commonfixed
points,forCq−commutingmapswhicharemoregeneralthanweaklycom-
patiblemaps,areobtainedinthesettingofaconvexmetricspace.Apply-
