NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS VOLUME 1

NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS VOLUME 1

CONTENTS

PREFACE

NEWABSTRACTCONVEXSPACESFORTHEKKMTHEORY

1.Introduction

2.Abstractconvexspaces

3.TheKKMspaces

4.Generalizedconvexspaces

5.Spaceshavingafamily{°A}A2hDi

References

STRONGCONVERGENCETHEOREMSOFCOMMONFIXEDPOINTSFORAFINITEFAMILYOFRELATIVELYNONEXPANSIVEMAPPINGS

1.Introduction

2.Preliminaries

3.ResultsonAlgorithmicConvergenceAnalysis

References

CONVERGENCEANALYSISFORSTEFFENSEN-LIKEMETHOD

1.Introduction

2.MajorizingSequences

3.SemilocalConvergenceAnalysisofMethod(2)-(3).

4.LocalConvergenceofMethod(2)-(3)

References

GENERALIZEDVARIATIONALINEQUALITIESINVOLVINGRELAXEDMONOTONEMAPPINGSANDNONEXPANSIVEMAPPINGSINHILBERTSPACES

1.Introduction

2.Preliminaries

3.Algorithms

4.MainResults

References

ITERATIVESCHEMESFORAFAMILYOFFINITEASYMPTOTICALLYPSEUDOCONTRACTIVEMAPPINGSINBANACHSPACES

1.Introduction

2.Preliminaries

3.MainResults

References

COMMONFIXEDPOINTTHEOREMSFORACLASSMAPSINL-FUZZYMETRICSPACES

1.IntroductionandPreliminaries

2.TheMainResults

References

FIXEDPOINTTHEOREMSINM-FUZZYMETRICSPACESWITHPROPERTY(E)

1.IntroductionandPreliminaries

2.TheMainResults

References

ONFIXEDPOINTTHEORYINWEAKLYCAUCHYNORMEDSPACES

1.Introduction

2.Preliminaries

3.FixedPointTheoryofContractionandNonexpansiveMappingsinWeaklyCauchyNormedSpaces

4.On{a,b,c}-Generalized-ContractionandGeneralized-NonexpansiveMappingsinWeaklyCauchyNormedSpaces

References

ASTRONGCONVERGENCETHEOREMFORNONEXPANSIVEMAPPINGS

1.IntroductionandPreliminaries

2.MainResults

References

THECONVERGENCEOFITERATIVESEQUENCEFORASYMPTOTICALLYDEMICONTRACTIVEMAPSINBANACHSPACES

1.Introduction

2.MainResults

References

ACHARACTERIZATIONOFUPPERSEMI-CONTINUITYOFTHESOLUTIONMAPTOTHEVERTICALIMPLICITHOMOGENEOUSF-COMPLEMENTARITYPROBLEMWITHR0-CONDITION

1.Introduction

2.VerticalImplicitF-ComplementarityProblems

3.MainResults

References

ISOMORPHISMSINBANACHALGEBRAS

1.IntroductionandPreliminaries

2.IsomorphismsinBanachAlgebras

3.DerivationsonBanachAlgebras

References

ONPOSITIVESOLUTIONSOFNONLINEARnth-ORDERSINGULARBOUNDARYVALUEPROBLEMWITHNONLOCALCONDITIONS

1.Introduction

2.PreliminariesandSeveralLemmas

3.ExistenceandNonexistenceofPositiveSolution

4.ExistenceofTwoPositiveSolutions

5.InfinitelyManyPositiveSolutions

References

ANELEMENTARYAPPROACHTOFIXEDPOINTINDEXFORCOUNTABLYCONDENSINGMAPS

1.Introduction

2.Single-valuedMaps

3.Multi-valuedMaps

References

STRONGCONVERGENCETHEOREMSOFTHECQMETHODFORSOLUTIONTOVARIATIONALINEQUALITIESINHILBERTSPACE

1.IntroductionandPreliminaries

2.MainResults

References

ONTHENEARESTCOMMONFIXEDPOINTPROBLEMFORANINFINITEFAMILYOFNON-SELFNONEXPANSIVEMAPPINGS

1.IntroductionandPreliminaries

2.MainResults

3.SomeApplicationsofTheorem2.2

References

ANOTEONUNIFORMCONVERGENCEOFITERATESOFASYMPTOTICCONTRACTIONS

1.Introduction

2.AGeneralizationofTheorem1.5

3.AnExtensionofTheorem2.1

4.AnotherVersionofTheorem1.2

References

COMPARATIVESTATIONARITYOFSTOCHASTICEXPONENTIALANDMONOMIALDENSITIESANDRELATEDNONLINEARAPPROXIMATIONS

1.IntroductionandPreliminaries

2.SubstationarityoftheX-and

2.1.TheX-and

2.2.U-andV-sequences

3.AsymptoticVarianceStationarityoftheX-and

4.Low-OrderFunctionalSplinesover[a,b]

4.1.OrthogonalizedDensities

4.2.CrossCorrelations

4.3.FunctionalSplines

References

OPTIMALCONTROLPROBLEMSFORSEMILINEARSECONDORDERVOLTERRAINTEGRO-DIFFERENTIALEQUATIONSINHILBERTSPACE

1.Introduction

2.VolterraIntegro-DierentialEquations

3.QuadraticOptimalControlProblems

4.AnApplicationtotheSemilinearwaveEquationwithaFadingMemory

References

SOMEPROPERTIESOFAGENERALIZEDFRACTIONALBROWNIANMOTION

1.Introduction

2.TheLocalNondeterminismofagfBm

3.TheJointlyContinuityoftheLocalTimeofagfBm

4.TheHausdorDimensionsoftheLevelSetsofagfBm

References

SOMECOMMONFIXEDPOINTTHEOREMSFORWEAKLYCOMMUTINGMAPPINGSINMENGERPROBABILISYICMETRICSPACES

1.IntroductionandPreliminaries

2.MainResults

References

GLOBALCONVERGENCETHEOREMSFORACCRETIVEANDPSEUDO-CONTRACTIVEMAPPINGS

1.Introduction

2.Preliminaries

3.MainResults

References

EXISTENCEOFSOLUTIONSFORNEWSYSTEMSOFGENERALIZEDQUASI-VARIATIONALINCLUSIONPROBLEMSINFC-SPACES

1.Introduction

2.Preliminaries

3.ExistenceofSolutionsfortheSGQVIPs

References

COMMONFIXEDPOINTSFORTWOPAIRSOFCOMPATIBLEMAPPINGSIN2-METRICSPACES

1.Introduction

2.Preliminaries

3.CommonFixedPointTheorems

References

GENERALIZEDCONTRACTIONMAPPINGPRINCIPLEINMENGERPROBABILISTICMETRICSPACES

1.IntroductionandPreliminaries

2.GeneralizedContractionMappingPrincipleinMengerPM-spaces

3.FixedPointTheoremsforCompatibleMappings

References