On Strongly Convex Sets and Farthest Distance Functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908476491431936 |
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| author | Martínez-Legaz, Juan Enrique |
| author_facet | Martínez-Legaz, Juan Enrique |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Strongly Convex Sets and Farthest Distance Functions Martínez-Legaz, Juan Enrique Functional Analysis Optimization and Control 52A05, 26B25 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. |
| title | On Strongly Convex Sets and Farthest Distance Functions |
| topic | Functional Analysis Optimization and Control 52A05, 26B25 |
| url | https://arxiv.org/abs/2507.15053 |