Banach空间中远达和同时远达问题的适定性

On Well Posedness of Farthest and Simultaneous Farthest Problems in Banach Spaces

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．

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.