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广义和强广义一致凸Banach空间 被引量:1

The generalized and strongly generalized uniform convex banach spaces
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摘要 引入了广义一致凸Banach空间和强广义一致凸Banach空间的概念,证明了一致凸Banach空间是强广义一致凸Banach空间,广义一致凸Banach空间X是弱局部一致凸和严格凸的;X中任一元在以0为顶点的闭凸锥中有惟一最佳逼近;强广义一致凸Banach空间中任一元在其闭凸子集中有惟一的最佳逼近元。 The definitions of generalized and strongly generalized uniform convex Banach spaces are given. We prove that uniform convex spaces are strongly generalized uniform convex spaces, and generalized uniform spaces are weak local uniform convex and strictly convex, and the closed convex cone with zero verzex of generalized uniform convex space X and closed convex subset of strongly generalized uniform convex space X_1 have one and only one best approximation for every x∈X and x∈X_1 respectively.
作者 孟京华
出处 《佛山科学技术学院学报(自然科学版)》 CAS 2003年第4期8-11,共4页 Journal of Foshan University(Natural Science Edition)
关键词 一致凸BANACH空间 广义一致凸Banach空间 强广义一致凸Banach空间 弱局部一致凸Banach空间 uniform convex Banach space generalized uniform convex Banach space strongly generalized uniform convex Banach space weak local uniformly convex Banach space
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