Contracting the maximal points of an ordered convex set

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Abstract

The maximal points of a nonempty closed bounded convex set in a reflexive Banach spare, 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.
Original languageEnglish
Pages (from-to)255-264
Number of pages10
JournalJournal of Convex Analysis
Volume10
Issue number1
Publication statusPublished - 2003

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Maximal Points
Ordered Set
Convex Sets
Uniformly Convex
Convex Cone
Bounded Set
Stefan Banach
Homotopy
Ordinary differential equation
Semigroup
Closed
Sufficient Conditions

Cite this

Contracting the maximal points of an ordered convex set. / Burton, G R.

In: Journal of Convex Analysis, Vol. 10, No. 1, 2003, p. 255-264.

Research output: Contribution to journalArticle

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