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\(k\)-denting points in Banach spaces. (English) Zbl 1201.46014

Summary: We introduce the notion of \(k\)-denting points as a generalization of denting points. We discuss its relationship with \(k\)-extreme points, \(H\)-points and \(k\)-strongly exposed points and prove that, if a Banach space \(X\) is reflexive, then \(X\) is \(k\)-strongly convex if and only if every point of \(S(X)\) is a \(k\)-denting point of \(U(X)\).

MSC:

46B09 Probabilistic methods in Banach space theory
46B20 Geometry and structure of normed linear spaces
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