KKM定理的推廣及應(yīng)用.pdf

1、目錄摘要……Abstract……11第一章緒論……第二章KKM定理的推廣及其應(yīng)用2.IG一凸空間中的廣義KKM定理……2.2L一凸空間中的廣義KKM定理……第三章FC一空間中較佳容許集值映射及應(yīng)用……19預(yù)備知識(shí)……193.2FC一空間中關(guān)于較佳容許集值映射的KKM型定理……203.3FC一空間中KKM型定理的應(yīng)用……25參考文獻(xiàn)……28致謝……32西南大學(xué)碩士學(xué)位論文Abstl公ctAbstractThisPaPermainlyfur

2、therstudiesseveralfoeusProblemsofnonlinearfunetionalanalysisinG一convexsPaces、L一eonvexsPaeesandfinitelyconiinuoustoPologiealsPaces(inshort，F(xiàn)C一sPaces)withoutanyconvexitvlinearstruCture，~e~KKM一t即etheoryareobtained.Theseresu

3、ltsunitesandgeneralizesomeknownresultsinreeeniliterature.InthefirstehaPter，wesimPlyintroducethebaekgroundoftheKKMtheoryanditsdevelopment.hitheseeondehaPter，firstly，byusingtransfereomPactlyoPen一valued(closed一valued)，thege

4、neralizedKKM一tyPetheemsinG一eonvexsPacesareprovedAsaPPlieations，someminimaxinequalitiesandexisteneeofmaximalelementsareobtainedinG一eonvexsPaces.Finally，newelassesofL一KKMmaPPings、generaiizedG~LKKMmaPPingsandgeneralizedG一S~

5、LKKMmaPPingsinanonemPtysubsetofaL一eonvexsPaceareobtained.SomenewgeneralizedL~KKMtheorems、G~LKKMtheoremsandgeneralizedG一S~LKKMtheoremsareestablishedunderthenoneomPaetsetingofaL一convexsPace.Byusingtheseresults，somemi苗maxin

6、equalitiesandsaddletheoremsareProvedinL一eonvexsPace.hithe而rdehaPter，weintroducetheneweoncePteoftheclassBfadmissibleset一valuedmaPPingsinFC一sPaees.With而5neweoneePt，somenewKKM一t即etheoremsinvolvingtheset一valuedmaPPingwitheom

7、PactlyloealinierseetionProPertyareProvedinFC一sPaces.ByaPPlyingtheKKM一tyPetheems，someneweoineideneetheoremsareobtainedinFC一sPacesundermuehweakassumPtions.Keywords:G一convexsPaceFC一sPaceK…KM一t即etheemadmissibleset一valuedmaPP