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Near smoothness, near convexity and drop properties and their applications. (Chinese. English summary) Zbl 0852.46012

Summary: This article discovers that, using (norm or weak) relative sequential compactness of sequences under some conditions, one can uniformly and most simply treat the concepts of locally uniform near smoothness, weak Hahn-Banach smoothness and drop property of Banach spaces. Starting with this, we deduce some new relationships among them and their new properties, and get some new equivalent conditions for the reflexivity of Banach spaces.

MSC:

46B20 Geometry and structure of normed linear spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
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