Displaying similar documents to “Some properties of convex functions of higher orders”

Convex transformations with Banach lattice range.

Roman Ger (1987)

Stochastica

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A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised...

Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

Studia Mathematica

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Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by K 0 the set of all X ∈ K() such that the farthest distance mapping a ↦ M X ( a ) is multivalued on a dense subset of . It is proved that K 0 is a residual dense subset of K().