| Banach空间中远达和同时远达问题的适定性 |
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| 引用本文： | 倪仁兴,李冲.Banach空间中远达和同时远达问题的适定性[J].数学学报,2000,43(3):421-426. |
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| 作者姓名： | 倪仁兴 李冲 |
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| 作者单位： | [1]绍兴文理学院数学系 [2]东南大学应用数学系 |
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| 基金项目： | 国家自然科学基金!（19971013），江苏省自然科学基金 |
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| 摘 要： | 本文研究Ｂａｎａｃｈ空间Ｘ中远达和同时远达问题的适定性，在集合的Ｈａｕｓ－ ｄｏｒｆｆ距离下，对Ｘ中的闭凸子集Ｄ和相对弱紧的有界闭子集Ｋ，证明了下述结果： 若Ｄ关于Ｋ严格凸和有Ｋａｄｅｃ性质，则Ｄ中所有使远达问题 ｍａｘ｛ｘ，Ｋ｝是适定的 点ｘ全体在Ｄ中是Ｇδ型集．作为应用，得到了同时远达问题适定性的类似结果．
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| 关 键 词： | 远达和同时远达问题 相对弱紧 适定性 |
On Well Posedness of Farthest and Simultaneous Farthest Problems in Banach Spaces |
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| NI Ren-xing.On Well Posedness of Farthest and Simultaneous Farthest Problems in Banach Spaces[J].Acta Mathematica Sinica,2000,43(3):421-426. |
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| Authors: | NI Ren-xing |
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| Institution: | NI Ren-xing (Deportment of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, P. R. China) LI Chong (Department of Applied Mathematics, Southeast University, Nanjing 210096, P. R. China) |
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| Abstract: | The well posedness of farthest and simultaneous farthest problems in Banach spaces X are investigated. Under the Hausdorff metric of subsets, for closed convex subset D and bounded closed, relatively weakly compact K in X, we proved that the set of all points in D such that the farthest problem ma-c{x, K} is well posed is a dense Ge subset in D provided that D is both strictly convex and Kadec with respect to K. As an application, we also obtain the corresponding results for the simultaneous farthest problems. |
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| Keywords: | Farthest and simultaneous farthest problems Relatively weakly compact Well posedness |
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