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 language | English |
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Pages (from-to) | 255-264 |
Number of pages | 10 |
Journal | Journal of Convex Analysis |
Volume | 10 |
Issue number | 1 |
Publication status | Published - 2003 |