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Examples of Convex Functions and Classifications of Normed Spaces

Borwein, Jonathan M. and Fitzpatrick, Simon and Vanderwerff, Jon D. (1994) Examples of Convex Functions and Classifications of Normed Spaces. Journal of Convex Analysis, 1 (1). pp. 61-73. ISSN 0944-6532

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      Abstract

      We study various properties of convex functions and their connections to the structure of the spaces on which they are defined. In particular, it is shown boundedness properties of convex functions on various bornologies are related to sequential convergence in dual topologies. Convex functions whose subdifferentials have range with nonconvex interior are constructed on nonreflexive spaces, and we exhibit examples of convex functions on infinite dimensional spaces whose subdifferentials have sparse domains.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: convex function, bounded subdifferential, domain, range, Mackey convergence, support points
      Subjects: 46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 16 Nov 2003
      Last Modified: 07 Sep 2014 20:20
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/64

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