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Boundedness, Differentiability and Extensions of Convex Functions

Borwein, Jonathan M. and Montesinos, Vicente and Vanderwerff, Jon D. (2006) Boundedness, Differentiability and Extensions of Convex Functions. J. Convex Analysis, 13 (3-4). pp. 587-602.

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    Abstract

    We survey various boundedness and differentiability properties of convex functions, and how they are related to sequential convergence with respect to various topologies in the dual space. We build on those techniques surveyed to provide a new characterization for extending continuous convex functions. As an application of this characterization, we prove if X/Y is separable, then every continuous convex function on Y can be extended to a continuous convex function on X.

    Item Type: Article
    Additional Information: pubdom TRUE
    Uncontrolled Keywords: Convex Function, Schur property, Dunford-Pettis property, Grothendieck property, Extensions
    Subjects: 46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
    49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
    90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
    52-xx Convex and discrete geometry > 52Axx General convexity
    46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 22 Mar 2005
    Last Modified: 12 Jan 2015 13:11
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/288

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