| On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces |
| |
| 作者姓名： | Chong LI Genaro LOPEZ |
| |
| 作者单位： | [1]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China [2]Department of Mathematic Analysis, University of Sevilla, Seville, Spain |
| |
| 基金项目： | The first author is supported in part by the National Natural Science Foundation of China （Grant No. 10271025）. The second author is supported in part by Projects BFM 2000-0344 and FQM-127 of Spain. |
| |
| 摘 要： | Let B （resp. K, BC,KC） denote the set of all nonempty bounded （resp. compact, bounded convex, compact convex） closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem （F, G） is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC ／ G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B ／B° （resp. K ／ B°, BC ／B°, KC ／ B°） is a-porous in B （resp. K,BC, KC）. Moreover, we prove that for most （in the sense of the Baire category） closed bounded subsets G of X, the set K ／ B° is dense and uncountable in K.
|
| 关 键 词： | Chebyshev中心点 不确定轨迹 非空界限 Banach空间 |
| 收稿时间： | 2003-08-21 |
| 修稿时间： | 2003-08-212004-06-18 |
On Generic Well–posedness of Restricted Chebyshev Center Problems in Banach Spaces |
| |
| Chong LI Genaro LOPEZ.On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces[J].Acta Mathematica Sinica,2006,22(3):741-750. |
| |
| Authors: | Chong Li Genaro Lopez |
| |
| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;(2) Department of Mathematic Analysis, University of Sevilla, Seville, Spain |
| |
| Abstract: | |
| |
| Keywords: | Chebyshev center Well– posedness σ – porous Ambiguous loci |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
