不动点理论导论

图书标准信息

• 作者 [美]伊斯特拉泰斯库 著
• 出版社 世界图书出版公司
• 出版时间 2009-05
• 版次 1
• ISBN 9787510004599
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 466页
• 正文语种 英语

【内容简介】

　　Thisbookisintendedasanintroductiontofixedpointtheoryanditsapplications.Thetopicstreatedrangefromfairlystandardresults（suchasthePrincipleofContractionMapping，BrouwersandSchaudersfixedpointtheorems）tothefrontierofwhatisknown，butwehavenottriedtoachievemaximalgeneralityinallpossibledirections.Wehopethatthereferencesquotedmaybeusefulforthispurpose.
　　Thepointofviewadoptedinthisbookisthatoffunctionalanalysis;forthereadersmoreinterestedinthealgebraictopologicalpointofviewwehaveaddedsomereferencesattheendofthebook.Aknowledgeoffunctionalanalysisisnotaprerequisite，althoughaknowledgeofanintroductorycourseinfunctionalanalysiswouldbeprofitable.However，thebookcontainstwointroductorychapters，oneongeneraltopologyandanotheronBanachandHilbertspaces.

【目录】

EditorsPreface
Foreword
CHAPTER1.TopologicalSpacesandTopologicalLinearSpaces
1.1.MetricSpaces
1.2.CompactnessinMetricSpaces.MeasuresofNoncompactness
1.3.BaireCategoryTheorem
1.4.TopologicalSpaces
1.5.LinearTopologicalSpaces.LocallyConvexSpaces

CHAPTER2.HilbertspacesandBanachspaces
2.1.NormedSpaces.BanachSpaces
2.2.HilbertSpaces
2.3.ConvergenceinX，X*andL(X)
2.4.TheAdjointofanOperator
2.5.ClassesofBanachSpaces
2.6.MeasuresofNoncompactnessinBanachSpaces
2.7.ClassesofSpecialOperatorsonBanachSpaces

CHAPTER3.TheContractionPrinciple
3.0.Introduction
3.1.ThePrincipleofContractionMappinginCompleteMetricSpaces
3.2.LinearOperatorsandContractionMappings
3.3.SomeGeneralizationsoftheContractionMappings
3.4.HilbertsProjectiveMetricandMappingsofContractiveType
3.5.ApproximateIteration
3.6.AConverseoftheContractionPrinciple
3.7.SomeApplicationsoftheContractionPrinciple

CHAPTER4.BrouwersFixedPointTheorem
4.0.Introduction
4.1.TheFixedPointProperty
4.2.BrouwersFixedPointtheorem.EquivalentFormulations
4.3.RobbinsComplementsofBrouwersTheorem
4.4.TheBorsuk-UlamTheorem
4.5.AnElementaryProofofBrouwersTheorem
4.6.SomeExamples
4.7.SomeApplicationsofBrouwersFixedPointTheorem
4.8.TheComputationofFixedPoints.ScarfsTheorem

CHAPTER5.SchaudersFixedPointTheoremandSomeGeneralizations
5.0.Introduction
5.1.TheSchauderFixedPointTheorem
5.2.DarbosGeneralizationofSchaudersFixedPointTheorem
5.3.Krasnoselskiis，RothesandAltmansTheorems
5.4.BrowdersandFansGeneralizationsofSchaudersandTychonoffsFixedPointTheorem
5.5.SomeApplications

CHAPTER6.FixedPointTheoremsjbrNonexpansiveMappingsandRelatedClassesofMappings
6.0.Introduction
6.1.NonexpansiveMappings
6.2.TheExtensionofNonexpansiveMappings
6.3.SomeGeneralPropertiesofNonexpansiveMappings
6.4.NonexpansiveMappingsonSomeClassesofBanachSpaces
6.5.ConvergenceofIterationsofNonexpansiveMappings
6.6.ClassesofMappingsRelatedtoNonexpansiveMappings
6.7.ComputationofFixedPointsforClassesofNonexpansiveMappings
6.8.ASimpleExampleofaNonexpansiveMappingonaRotundSpaceWithoutFixedPoints

CHAPTER7.SequencesofMappingsandFixedPoints
7.0.Introduction
7.1.ConvergenceofFixedPointsforContractionsorRelatedMappings
7.2.SequencesofMappingsandMeasuresofNoncompactness

CHAPTER8.DualityMappingsamtMonotomeOperators
8.0.Introduction
8.1.DualityMappings
8.2.MonotoneMappingsandClassesofNonexpansiveMappings
8.3.SomeSurjectivityTheoremsonRealBanachSpaces
8.4.SomeSurjectivityTheoremsinComplexBanachSpaces
8.5.SomeSurjectivityTheoremsinLocallyConvexSpaces
8.6.DualityMappingsandMonotonicityforSet-ValuedMappings
8.7.SomeApplications

CHAPTER9.FamiliesofMappingsandFixedPoints
9.0.Introduction
9.1.MarkovsandKakutanisResults
9.2.TheRylI-NardzewskiFixedPointTheorem
9.3.FixedPointsforFamiliesofNonexpansiveMappings
9.4.lnvariantMeansonSemigroupsandFixedPointforFamiliesofMappings

CHAPTER10.FixedPointsandSet-ValuedMappings
10.0Introduction
10.1ThePompeiu-HausdorffMetric
10.2.ContinuityforSet-ValuedMappings
10.3.FixedPointTheoremsforSomeClassesofSet-valuedMappings
10.4.Set-ValuedContractionMappings
10.5.SequencesofSet-ValuedMappingsandFixedPoints

CHAPTER11.FixedPointTheoremsforMappingsonPM-Spaces
11.0.Introduction
11.1.PM-Spaces
11.2.ContractionMappingsinPM-Spaces
11.3.ProbabilisticMeasuresofNoncompactness
11.4.SequencesofMappingsandFixedPoints

CHAPTER12.TheTopologicalDegree
12.0.Introduction
12.1.TheTopologicalDegreeinFinite-DimensionalSpaces
12.2.TheLeray-SchauderTopologicalDegree
12.3.LeraysExample
12.4.TheTopologicalDegreefork-SetContractions
12.5.TheUniquenessProblemfortheTopologicalDegree
I2.6.TheComputationoftheTopologicalDegree
12.7.SomeApplicationsoftheTopologicalDegree
BIBLIOGRAPHY
INDEX