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Generic differentiability of order-bounded convex operators

Borwein, Jonathan M. (1986) Generic differentiability of order-bounded convex operators. Journal of the Australian Mathematical Society: Series B: Applied Mathematics, 23 . pp. 22-29.

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    Abstract

    We give sufficient conditions for order-bounded convex operators to be generically differentiable (Gâteaux or Fréchet). When the range space is a countably order-complete Banach lattice, these conditions are also necessary. In particular, every order-bounded convex operator from an Asplund space into such a lattice is generically Fréchet differentiable, if and only if the lattice has weakly-compact order intervals, if and only if the lattice has strongly-exposed order intervals. Applications are given which indicate how such results relate to optimization theory.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 20 Feb 2015 17:02
    Last Modified: 20 Feb 2015 17:02
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1607

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