Common Fixed Point Theorems in Complete Menger PM-spaces.pdf

1、亨689907CommonFixedPointTheoremsinCompleteMengerPMspacesCommonFixedPointTheoremsinCompleteMengerPMspacesFengrongZhangSuperviser:AssociateProfessorZeqingL.iuBasicMathematicsNonlinearAnalysisIntroductionLCommonFixedPointThe

2、oremsforMultivaluedMappingsinMengerPMspace1.1PreliminariesLet(XFA)。。。MongerPMspace。，th。。mtinuoustnorm△。、。Abe。nonemptysubsetofX工fsup巧(，)=I，whereDt(1)二‘中0calledaprobabilisticallyboundedsetsup惑’Js)thenA’A應(yīng)andD.小heprobabilis

3、ticdiameter。。LemmaI.1.1.[41Let(XFA)be。Mongeri14spacewi。，、。。。。:，。。。。、:一。、IfAisaprobabilisticallyboundedsetthenD.(t)isadistributionfunctionIfABCXareprobabilisticallyboundedsetsthenAvt3isalsoaprobabilisticallyboundedset(I)(

4、2)isthefamilyofallandA〔0nonemptyTclosedprobabilisticallyboundedsets.FortheprobabilisticdistancebetweenxandAisthefunction凡，只萬letxECommonFixedPointTheoremsinCompleteMcngerPMspaces(s)anysupillf萬七月EB凡whichshowsthatxcAandyEBH

5、ence一supF(1)一F_(t)for=此湯(t)isBythedefinitionA二Beasytoseethatitiseasytosee1foranyt0.nondecreasingandDAB(0)=0樹幾氣A=B=x，。IJ(2)andleftcontinuousatt.NowweprovethatsupDAB(l)=nn卜triceAuBAandBalsoisareprobabilisticallyboundedfrom

6、IenunaI.Lt(2)wehavethatprobabilisticallyboundedandsosupD.(，)=supsup產(chǎn)o‘全supsup!0..sup凡52弓矛1十2sup叭心、、氣刁”△認(rèn)I(.)F:JIAA(FfjFy(sz))sup氣吠!l聲2刊任月工infzEAVEH△〔infA..CF，(sI:infzECye8Fy(一習(xí)二5叩凡0.1.1..itis(’)DwA(t)于T.A(2)Letipandseeth