-convexity and best approximation.

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.

The convexity of the subset space of a metric space

V. W. Bryant (1970)

Compositio Mathematica

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Best coapproximation in metric spaces.

Narang, T.D. (1992)

Publications de l'Institut Mathématique. Nouvelle Série

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Selections and near-selections in metric linear spaces without local convexity

Tadeusz Dobrowolski, Jan van Mill (2006)

Fundamenta Mathematicae

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We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.

A "hidden" characterization of polyhedral convex sets

Taras Banakh, Ivan Hetman (2011)

Studia Mathematica

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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.

On convex metric spaces V

R. Duda (1970)

Fundamenta Mathematicae

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