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Abstract
This note is concerned with proximinality and best proximity pair theorems in hyperconvex metric spaces and in Hilbert spaces. Given two subsets A and B of a metric space and a mapping best proximity pair theorems provide sufficient conditions that ensure the existence of an
such that
Acknowledgment
The work of the second author was partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund.
Notes
aA Banach space is hyperconvex if and only if it is isometrically isomorphic to a space of continuous functions on a stonian space K (see, e.g., Schaefer (1974))