Proximinal Retracts and Best Proximity Pair Theorems

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 Thus such theorems provide optimal approximate solutions in the case that the mapping T does not have fixed points.

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