锥b-度量空间中广义拟压缩映射的不动点定理.pdf

应 用 数 学 MATHEMATICA APPLICATA 2Ol4。27(4)：755—762 FixedPointTheoremsforGeneralized Quasi-c‘ontractiveMapsinConeb-—metricSpaces SHILu(石露)，XUShaoyuan(许绍元) (1．SchoolofMathematicsandStatistics，HubeiNormalUniversity，Huangshi435002，Chi— na；2．DepartmentofMathematicsandStatistics，HanshanNormalUniversity，Chaozhou 52104l，China) Abstract：In201l，HussainandShahandZHANG introducedconeb—metriespacesandgeneralized quasi—contractionsrespectively．Theformerobtained sometopologicalpropertiesofconeb-metric spaces，whilethelattergottheuniquefixedpointresultsinconemetricspaceswiththeassumption ofnormality．FollowingHussainandShahandZHANG，thepresentpaperwillshow fixedpointthe— oremsforself—mappingssatisfyinggeneralizedquasi—contractiveconditionwiththeconstant ∈ (O， 1／s)inconeb～metricspaceswithouttheassumptionofnormality，wherethecoefficient5satisfies ≥ 1．Ourmainresultsimproveandgeneralizesomerelatedresultsintheliterature． Keywords：Fixedpoint；Generalizedquasi—contraction；Coneb—metricspace CLCNumber：O177．91 AMS(2000)SubjectClassification：54H25；47H10 DOCUmentcode：A ArticleID：1OO1—9847(2014)04-0755一O8 1．IntroductiOn HUANG LongguangandZHANG Xian[川 introducedtheconceptofconemetricspace， describedthepropertiesofsequenceson conemetricspacesandprovedvariousfixedpoint theoremsforcontractivemappings[2-6]Also，D．IlicandV．Rakocevic[]introducedquasi—con— ． tractionOnconemetricspacesandsomeauthorsobtainedafew resultswithoutthenormal cone，butonlyinthecaseofacontractiveconstant ∈ (0，1／2)．L．GajicandV．Rakocevic[ provedthatresultistruefor ∈ (O，1)onconemetricspacesbyanew way．ZHANG Xian[] introducedseveralmeaningfulfixedpointresultsforonegeneralizedquasi——contractivemap—— ping．However，therearefew resultsaboutgeneralizedquasi—contractivemappings．Recently， N．HussainandM ．H．ShahE]introducedconeb—metricspaces．asagen