出版社：世界图书出版公司北京公司
年代：2009
定价：59.0
本书是一部介绍不动点理论及其应用的入门教程。内容范围广阔，但并不是为增加书的篇幅而包括所有可能的结果，涉及从经典标准结果到最新前沿成果。
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.FixedPointTheoremsforNonexpansiveMappingsandRelatedClassesofMappings
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.DualityMappingsandMonotoneOperators
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.TheRyll-NardzewskiFixed~PointTheorem
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-SchauderTopo!ogicalDegree
12.3.LeraysExample
12.4.TheTopologicalDegreefork-SetContractions
12.5.TheUniquenessProblemfortheTopologicalDegree
12.6.TheComputationoftheTopologicalDegree
12.7.SomeApplicationsoftheTopologicalDegree
BIBLIOGRAPHY
INDEX
Thisbookisintendedasanintroductiontofixedpointtheoryanditsapplications.Thetopicstreatedrangefromfairlystandardresults(suchasthePrincipleofContractionMapping,BrouwersandSchaudersfixedpointtheorems)tothefrontierofwhatisknown,butwehavenottriedtoachievemaximalgeneralityinallpossibledirections.Wehopethatthereferencesquotedmaybeusefulforthispurpose.
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 59.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
不动点理论是世界图书出版公司北京公司于2009.05出版的中图分类号为 O189.2 的主题关于 不动点定理－英文 的书籍。