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arXiv · 2507.15053

On Strongly Convex Sets and Farthest Distance Functions

Juan Enrique Martínez-Legaz
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Abstract

A polarity notion for sets in a Banach space is introduced in such a way that the second polar of a set coincides with the smallest strongly convex set with respect to R that contains it. Strongly convex sets are characterized in terms of their associated farthest distance functions, and farthest distance functions associated with strongly convex sets are characterized, too.

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Juan Enrique Martínez-Legaz. 2025-07-20. On Strongly Convex Sets and Farthest Distance Functions. https://arxiv.org/abs/2507.15053

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