摘要
设C是实Banach空间X中有界闭凸子集且O是C的内点,G是X中非空有界闭的相对弱紧子集.记K(X)为X的非空紧凸子集并赋Hausdorff距离.称广义共同远达点问题max_c(A,G)是适定的是指它有惟一解(x_0,z_0)且它的每个极大化序列均强收敛到(x_0,z_0).在C是严格凸和Kadec的假定下,运用不同于De Blasi,Myjak and Papini和Li等人的方法证明了集{A∈K(X);max_c(A,G)是适定的}含有K(X)中稠G_δ集,这本质地推广和延拓了包括De Blasi,Myjak and Papini和Li等人在内的近期相应结果.
Abstract
Let C be a closed bounded convex subset of a real Banach space X with o being an interior point of C.Let G be a nonempty bounded closed relatively weakly compact subsets of X.Let K(X) denote the space of all nonempty compact convex subset of X endowed with the Hausdorff distance.A generalized mutually furthest points problem mac_c(A,G),is said to be well posed if it has a unique solution (x_0,z_0).and every maximizing sequence converges strongly to (x_0,z_0).Under the assumption that C is strictly convex and (sequentially) Kadec we,adopting a different approach in [1] and [2],prove that the set {A∈K(X);max_c(A,G) is well posed} contains a dense G_δ-subset of K(X).Our results generalize and extend the recent corresponding results due to De Blasi,Myjak and Papini,Li and other authors.
关键词
广义共同远达点问题 /
严格凸和Kadec /
适定性
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Key words
Generalized mutually furthest points problem /
strictly convex and (sequentially) Kadec
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倪仁兴.
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非自反实Banach空间中的广义共同远达点问题的适定性. 系统科学与数学, 2001, 21(3): 335-342. https://doi.org/10.12341/jssms09723
Ren Xing NI.
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ON WELL POSEDNESS OF GENERALIZED MUTUALLY FURTHEST POINTS PROBLEM IN A NONREFLEXIVE REAL BANACH SPACE. Journal of Systems Science and Mathematical Sciences, 2001, 21(3): 335-342 https://doi.org/10.12341/jssms09723
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脚注
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