不動點定理的一些等價形式及推廣.pdf

1、分類號：Q225論文編號：蛆Q2Q281Y；960386密級：公玨貴州大學2006屆碩士研究生學位論文論文題目不動點定理的一些等價形式及推廣學科專業(yè)：運籌學與控制論研究方向：非線性分析與對策論導師：俞建教授曹素元教授研究生：鄭桂梅中國貴州貴陽2006年5月貴州大學碩士學位論文ABSTRACTFixedpoimtheoryhasbecomethemaincomponentofNonlinearAnanlysisItisappliedsuc

2、cessfullyinmanyfieldssuchaspartialdifferentialequation，cybernetics，economicbalancetheory，gametheoryandSOonInthisthesis，firstlywediscusssomefixedpointtheoremsandtheirequivalentformsAndthen，weestablishsomenewfixedp0砬theore

3、msandsectiontheoremsinHspaceandgivesomeapplicationsThisthesisconsistsofthreechaptersInchapterone，wesimplyintroducesomegeneralconceptsandpropositionsaboutconvexanalysis，topolopyspaceandsetvaluedmappingsInchaptertwo，wedisc

4、usssomeequivalentformsoffixedpointtheoremsFisrtlywesimplyintroducesomeimportantgeneralizationsofBrouwerfixedpointtheoremAndthen，weobtainthatBrouwerfixedpointtheorem，KKMtheorem，F(xiàn)KKMtheorem，KyFanminimaxinequalityBrowderfix

5、edpointtheorem，KyFaninequalityIthegeometryformofKyFanminimax，KyFansectiontheorem，F(xiàn)anBrowderfixedpointtheoremandKyFaninequalityIIareallequivalentInchapterthree，firstly，weintroducesomeimportantconceptsaboutH—spaceAndthenwe

6、obtainanewfixedpointtheoremofFanBrowdertypeinHspaceandsomeequivalentformsAsapplication，theseresultsareutilizedtostudytheexistenceproblemsoffixedpointandnearestpointinHspaceTheseresultsaregeneralizationsofZhang(1999)inH—s

7、paceFinallyweestablishanewsectiontheoremofFanHatypeinlocallyconvexH—spaceandsomecorrespondingequivalentversionsAsapplications，someminimaxtheoremsinHspaceareobtainedTheaboveresultsimproveandextendthecorrespondingresultsin