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＜E-Book＞
Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems / by I. Cioranescu
(Mathematics and Its Applications ; 62)

Edition	1st ed. 1990.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1990
Language	English
Size	XIV, 260 p : online resource
Authors	*Cioranescu, I author SpringerLink (Online service)
Subjects	LCSH:Functional analysis LCSH:Operator theory LCSH:Differential equations FREE:Functional Analysis FREE:Operator Theory FREE:Differential Equations
Notes	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 HTTP:URL=https://doi.org/10.1007/978-94-009-2121-4

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