I. Cioranescu

Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (eBook, PDF)

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 260
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789400921214
• Artikelnr.: 44047381

Inhaltsangabe

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.