Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems by I. CioranescuGeometry of Banach Spaces, Duality Mappings and Nonlinear Problems by I. Cioranescu

Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems

byI. Cioranescu

Paperback | January 10, 2012

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Title:Geometry of Banach Spaces, Duality Mappings and Nonlinear ProblemsFormat:PaperbackDimensions:260 pagesPublished:January 10, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401074542

ISBN - 13:9789401074544


Table of Contents

I. Subdifferentiability and Duality Mappings.- § 1. Generalities on convex functions.- § 2. The subdifferential and the conjugate of a convex function.- § 3. Smooth Banach spaces.- § 4. Duality mappings on Banach spaces.- § 5. Positive duality mappings.- Exercises.- Bibliographical comments.- II Characterizations of Some Classes of Banach Spaces by Duality Mappings.- § 1. Strictly convex Banach spaces.- § 2. Uniformly convex Banach spaces.- § 3. Duality mappings in reflexive Banach spaces.- § 4. Duality mappings in LP-spaces.- § 5. Duality mappings in Banach spaces with the property (h) and (?)1.- Exercises.- Bibliographical comments.- III Renorming of Banach Spaces.- § 1. Classical renorming results.- § 2. Lindenstrauss' and Trojanski's Theorems.- Exercises.- Bibliographical comments.- IV On the Topological Degree in Finite and Infinite Dimensions.- § 1. Brouwer's degree.- § 2. Browder-Petryshyn's degree for A-proper mappings.- § 3. P-compact mappings.- Exercises.- Bibliographical comments.- V Nonlinear Monotone Mappings.- § 1. Demicontinuity and hemicontinuity for monotone operators.- § 2. Monotone and maximal monotone mappings.- § 3. The role of the duality mapping in surjectivity and maximality problems.- § 4. Again on subdifferentials of convex functions.- Exercises.- Bibliographical comments.- VI Accretive Mappings and Semigroups of Nonlinear Contractions.- § 1. General properties of maximal accretive mappings.- § 2. Semigroups of nonlinear contractions in uniformly convex Banach spaces.- § 3. The exponential formula of Crandall-Liggett.- § 4. The abstract Cauchy problem for accretive mappings.- § 5. Semigroups of nonlinear contractions in Hilbert spaces.- § 6. The inhomogeneous case.- Exercises.- Bibliographical comments.- References.