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.

Author information

Contact details are reproduced from the original publication and may be historical.

Jon Borwein

Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6

Simon Fitzpatrick

Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia

Jon Vanderwerff

Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6

Keywords

  • Convex function
  • bounded subdifferential
  • domain
  • range
  • Mackey convergence
  • support points

Suggested citation

J. Borwein, S. Fitzpatrick, J. Vanderwerff. “Examples of Convex Functions and Classifications of Normed Spaces.” Journal of Convex Analysis 1 (1994), No. 1, 61–73. https://doi.org/10.68381/jca01004

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press.