Abstract

The maximal points of a nonempty closed bounded convex set in a reflexive Banach space, relative to an ordering defined by a locally uniformly convex cone, are studied. The set of maximal points is proved to be contractible, and sufficient conditions are found for it to be contractible by a homotopy with the semigroup property, or by the flow of an ordinary differential equation.

Author information

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

G. R. Burton

Dept. of Mathematical Sciences, University of Bath, Claverton Down, Bath
BA2 7AY, United Kingdom

Keywords

  • Order
  • cone
  • contractible convex set
  • flow

Mathematics Subject Classification

52A20, 46B20, 34C99

References

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Suggested citation

G. R. Burton. “Contracting the Maximal Points of an Ordered Convex Set.” Journal of Convex Analysis 10 (2003), No. 1, 255–264. https://doi.org/10.68381/jca1014

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.