Lipschitz Functions [electronic resource] / by Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae.
Material type:
TextSeries: Lecture Notes in Mathematics ; 2241Publisher: Cham : Springer International Publishing : Imprint: Springer, 2019Edition: 1st ed. 2019Description: XIV, 593 p. 2 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783030164898Subject(s): Functional analysis | Functions of real variables | Approximation theory | Operator theory | Convex geometry | Discrete geometry | Functional Analysis | Real Functions | Approximations and Expansions | Operator Theory | Convex and Discrete GeometryAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.7 LOC classification: QA319-329.9Online resources: Click here to access online
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Springer eBooksSummary: The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.