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Differentiability of cone-monotone functions in Banach spaces

Borwein, Jonathan M. and Burke, James V. and Lewis, Adrian (2003) Differentiability of cone-monotone functions in Banach spaces. Proceedings of the American Mathematical Society, 132 (4). pp. 1067-1076. ISSN 0002-9939

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    Abstract

    Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lipschitz functions, and necessary. We show by way of example that most results fail more generally.

    Item Type: Article
    Additional Information: pubdom FALSE
    Uncontrolled Keywords: Monotone functions, ordered Banach spaces, generating cones, differentiability
    Subjects: 46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
    46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    46-xx Functional analysis > 46Txx Nonlinear functional analysis
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 20 Nov 2003
    Last Modified: 12 Jan 2015 15:39
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/123

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