{"ID":2892652,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15053","arxiv_id":"2507.15053","title":"On Strongly Convex Sets and Farthest Distance Functions","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.","short_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 ass...","url_abs":"https://arxiv.org/abs/2507.15053","url_pdf":"https://arxiv.org/pdf/2507.15053v2","authors":"[\"Juan Enrique Martínez-Legaz\"]","published":"2025-07-20T17:20:28Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.OC\"]","methods":"[]","has_code":false}