不動(dòng)點(diǎn)定理的一些等價(jià)形式及推廣.pdf

1、分類號(hào)：Q225論文編號(hào)：蛆Q2Q281Y；960386密級(jí)：公玨貴州大學(xué)2006屆碩士研究生學(xué)位論文論文題目不動(dòng)點(diǎn)定理的一些等價(jià)形式及推廣學(xué)科專業(yè)：運(yùn)籌學(xué)與控制論研究方向：非線性分析與對(duì)策論導(dǎo)師：俞建教授曹素元教授研究生：鄭桂梅中國(guó)貴州貴陽(yáng)2006年5月貴州大學(xué)碩士學(xué)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