On convex metric spaces V

We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.

Strictly convex metric spaces with round balls and fixed points

Inese Bula (2005)

Banach Center Publications

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The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.

On order and metric convexities in $Z^{n}$

M. Changat, A. Vijayakumar (1992)

Compositio Mathematica

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Connexions between convexity of a metric continuum $X$ and convexity of its hyperspaces $C (X)$ and $2^{X}$

Duda, R.

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On Convex Sets with Convex-Hereditary CEP

Tadeusz Dobrowolski (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.

On some aspects of Jensen-Menger convexity.

Joanna Ger, Roman Ger (1992)

Stochastica

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The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.