The Variable Radius Form of the Extended Exterior Sphere Condition
Journal of Convex Analysis (2025) We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothing but the union of closed balls with lower semicontinous radius function. This general...
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| creator | Nour, Chadi Takche, Jean |
| description | Journal of Convex Analysis (2025) We introduce a variable radius form of the extended exterior sphere condition
of [16], and then, we prove that the complement of a closed set satisfying this
new property is nothing but the union of closed balls with lower semicontinous
radius function. This generalizes, to the variable radius case, the main result
of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in
[14,15] for prox-regularity, the exterior sphere condition, and the union of
closed balls property, we prove that the constant and the variable radius forms
of the extended exterior sphere condition belong to the S-convexity regularity
class. |
| doi_str_mv | 10.48550/arxiv.2403.04707 |
| format | Article |
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of [16], and then, we prove that the complement of a closed set satisfying this
new property is nothing but the union of closed balls with lower semicontinous
radius function. This generalizes, to the variable radius case, the main result
of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in
[14,15] for prox-regularity, the exterior sphere condition, and the union of
closed balls property, we prove that the constant and the variable radius forms
of the extended exterior sphere condition belong to the S-convexity regularity
class.</description><identifier>DOI: 10.48550/arxiv.2403.04707</identifier><language>eng</language><subject>Mathematics - Metric Geometry</subject><creationdate>2024-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2403.04707$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2403.04707$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Nour, Chadi</creatorcontrib><creatorcontrib>Takche, Jean</creatorcontrib><title>The Variable Radius Form of the Extended Exterior Sphere Condition</title><description>Journal of Convex Analysis (2025) We introduce a variable radius form of the extended exterior sphere condition
of [16], and then, we prove that the complement of a closed set satisfying this
new property is nothing but the union of closed balls with lower semicontinous
radius function. This generalizes, to the variable radius case, the main result
of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in
[14,15] for prox-regularity, the exterior sphere condition, and the union of
closed balls property, we prove that the constant and the variable radius forms
of the extended exterior sphere condition belong to the S-convexity regularity
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of [16], and then, we prove that the complement of a closed set satisfying this
new property is nothing but the union of closed balls with lower semicontinous
radius function. This generalizes, to the variable radius case, the main result
of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in
[14,15] for prox-regularity, the exterior sphere condition, and the union of
closed balls property, we prove that the constant and the variable radius forms
of the extended exterior sphere condition belong to the S-convexity regularity
class.</abstract><doi>10.48550/arxiv.2403.04707</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Metric Geometry |
| title | The Variable Radius Form of the Extended Exterior Sphere Condition |
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