半序空间的拓扑结构、不动点与优化问题

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ǤFÏ:2018c3‰FFÏ:2018c5TOPOLOGICALSTRUCTURES!FIXEDPOINTSANDOPTIMIZATIONPROBLEMSONPARTIALLYORDEREDSPACESADissertationSubmittedtoNanjingUniver

2、sityofFinanceandEconomicsFortheAcademicDegreeofMasterofScienceBYSaiLiSupervisedbyProfessorCongjunZhangSchoolofFinanceNanjingUniversityofFinanceandEconomicsMay2018ÆØ©ÕM5(²Ø©´·‡<3“•e?1ïÄóŠ9ïĤJ"Ø©¥ØAO±I5Ú—/•§Ø•¹Ù¦<½Ù§Å®²uL½>LïĤJ"Ù¦Ó“éïÄéuÚ¤‰zþ®3Ø©¥Š²((²¿L

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4、ÝþrcpÑbÝþ˜m†5IbÝþ˜mäkƒÓÿÀ(.ØÄ:¯K,C´iri´cÚ?[ØVg¿…˜‡š~ͶØÄ:(J,C´iri´c(J±ˆ«/ªí2.Š˜J´,P.D.Proinovïʇ[Øa.N¿…)û˜‡úm¯K,M.Cvetkovi´cïÄPerova.[Ø¿…˜'u‚5Žf(J.ùp·‚3IbÝþ˜mµee,ïÄAa•˜„[Øa.N,A‡'uØÄ:!ú
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6、•¼,ò8Š`z¯K=z•þï¯K,?ïĹå8Š`z¯Kf¿©)•35Ú[8Š`z¯Kr%C)NþŒëY5†eŒëY5.©í2!U?!Ú˜Cσ'©z˜(J.'…cµŒS˜m¶`z¯K¶ØÄ:¶ÿÀ(¶Iþ•¼IABSTRACTInthispaper,westudytopologicalstructures,optimizationandfixedpointsprob-lems.Morespecially,Partiallyorderedspacesreferstoconeb-metricspacesandpar-tial

7、lyorderedtopologicalvectorspacesinthispaper.Topologicalstructures.Let(X;d;K)beaconeb-metricspaceoveraorderedBa-nachspace(E;)withrespecttoconeP.Weintroduceab-metricrcandweprovethattheb-metricspaceinducedbyb-metricrchasthesametopologicalstructureswiththeconeb-metricspace.F

8、ixedPoints.C´iri´cintroducedtheconceptofquasi-contractionandobtainedawellknownfixedpointtheoreminthesettingofmetricspaces.ThenC´iri´c’sresulthasbeenextendedinmanydirections.ItisworthmentioningthatP.D.Proinovstudiedaquasi-contractiontypemappingandsolvedaopenproblem,M.Cvetko

9、vi´cresearchedquasi-contractionofPerovtypeandgotsomeimportantresultsconcerninglinearoperators.We