非线性泛函分析及其应用．第1卷，不动点定理

PrefacetotheSecondCorrectedPrinting

PrefacetotheFirstPrinting

Introduction

FUNDAMENTALFIXED-POINTPI~INCIPLES

CHAPTER1TheBanachFixed-PointTheoremandIterativeMethods

1.1.TheBanachFixed-PointTheorem

1.2.ContinuousDependenceonaParameter

1.3.TheSignificanceoftheBanachFixed-PointTheorem

1.4.ApplicationstoNonlinearEquations

1.5.AcceleratedConvergenceandNewtonsMethod

1.6.ThePicard-Lindel6fTheorem

1.7.TheMainTheoremforIterativeMethodsforLinearOperatorEquations

1.8.ApplicationstoSystemsofLinearEquations

1.9.ApplicationstoLinearIntegralEquations

CHAPTER2TheSchauderFixed-PointTheoremandCompactness

APPLICATIONSOFTHEFUNDAMENTALFIXED-POINTPRINCIPLES

CHAPTER3OrdinaryDifferentialEquationsinB-spaces

CHAPTER4DifferentialCalculusandtheImplicitFunctionTheorem

CHAPTER5NewtonsMethod

CHAPTER6ContinuationwithRespecttoaParameter

CHAPTER7PositiveOperators

CHAPTER8AnalyticBifurcationTheory

CHAPTER9FixedPointsofMultivaluedMaps

CHAPTER10NonexpansiveOperatorsandItertiveMethods

CHAPTER11CondensingMapsandtheBourbaki-KneserFixed-PointTheorem

THEMAPPINGDEGREEANDTHEFIXED-POINTINDEX

Appendix

References

AdditionalReferencestotheSecondPrinting

ListofSymbols

ListofTheorems

ListoftheMostImportantDefinitions

SchematicOverviews

GeneralReferencestotheLiterature

ListofImportantPrinciples

ContentsoftheOtherParts

Index

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