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Proximinal retracts and best proximity pair theorems. (English) Zbl 1054.47040

The authors study the existence of a proximinal retraction (also called metric projection) in hyperconvex metric spaces. Several interesting geometrical properties are proved.

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54C25 Embedding
52A99 General convexity
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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