Characterizations of some rotundity properties in terms of farthest points
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912621340393472 |
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| author | C, Arunachala Prasath Thota, Vamsinadh |
| author_facet | C, Arunachala Prasath Thota, Vamsinadh |
| contents | We characterize rotund, uniformly rotund, locally uniformly rotund and compactly locally uniformly rotund spaces in terms of sets of (almost) farthest points from the unit sphere using the generalized diameter. For this we introduce few remotality properties using the sets of almost farthest points. As a consequence, we obtain some characterizations of the aforementioned rotundity properties in terms of existing proximinality notions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizations of some rotundity properties in terms of farthest points C, Arunachala Prasath Thota, Vamsinadh Functional Analysis 46B20, 41A65, 41A52 We characterize rotund, uniformly rotund, locally uniformly rotund and compactly locally uniformly rotund spaces in terms of sets of (almost) farthest points from the unit sphere using the generalized diameter. For this we introduce few remotality properties using the sets of almost farthest points. As a consequence, we obtain some characterizations of the aforementioned rotundity properties in terms of existing proximinality notions. |
| title | Characterizations of some rotundity properties in terms of farthest points |
| topic | Functional Analysis 46B20, 41A65, 41A52 |
| url | https://arxiv.org/abs/2409.08697 |