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完備なBusemann空間の一様凸性
https://doi.org/10.34447/00001003
https://doi.org/10.34447/00001003fd933f1d-376f-4c18-b2d0-526677528cfc
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
kiyo27_41-48 (264.8 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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| 公開日 | 2023-03-10 | |||||||
| タイトル | ||||||||
| タイトル | 完備なBusemann空間の一様凸性 | |||||||
| 言語 | ja | |||||||
| タイトル | ||||||||
| タイトル | Uniform convexity of complete Busemann spaces | |||||||
| 言語 | en | |||||||
| 言語 | ||||||||
| 言語 | jpn | |||||||
| キーワード | ||||||||
| 主題 | Busemann space, uniformly convex, convex combination | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| ID登録 | ||||||||
| ID登録 | 10.34447/00001003 | |||||||
| ID登録タイプ | JaLC | |||||||
| 著者 |
冨澤, 佑季乃
× 冨澤, 佑季乃
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| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Normed linear spaces play an important role in pure and applied mathematics. In particular, Banach spaces are useful tools for problem-solving in computational science. Mathematicians have showed the geometric structure of Banach spaces since the introduction of uniform convexity by J. A. Clarkson. B. Beauzamy presented a characterization of uniform convexity of Banach spaces. This result was an important property to elucidate the geometric struc ture of Banach spaces. It contributed to solve various optimization problems. On the other hand, H. Busemann constructed a theory of non-positive curvature of metric spaces. Using this theory, B. H. Bowditch introduced nonpositive curvature spaces called Busemann spaces. Busemann spaces are more general than strictly convex Banach spaces. In recent years, Busemann spaces have attracted attention for their use in computational science. Against this background, the study of the geometric structure of Busemann spaces is valuable of pure and applied mathematics. In this paper, I discuss uniform convexity of complete Busemann spaces. As a main result, I prove a characterization of uniform convexity of Busemann spaces. This is a generalization of the characterization of uniform convexity of Banach spaces given by Beauzamy. |
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| 書誌情報 |
新潟工科大学研究紀要 巻 27, p. 41-48, 発行日 2023-03 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 1342-792X | |||||||
| 書誌レコードID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN10590360 | |||||||
| 著者版フラグ | ||||||||
| 出版タイプ | VoR | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||
| 出版者 | ||||||||
| 出版者 | 新潟工科大学 | |||||||
