The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space
---Publisher, magazine: ,
Publication year: 2002
Lưu Trích dẫn Chia sẻAbstract
A Banach space \(X\) is uniformly convex if and only if the duality mapping \(J:X\to 2^{X^n}\) is, in some sense, uniformly strictly monotone. Also the uniform convexity of \(X\) can be characterized via the normalized duality mapping \(J_p\), in a similar way. The author obtains such characterizations and applies them to study the continuity of the metric projection onto a family of closed convex sets in \(X\).
Tags: uniformly convex; duality mapping; uniform continuity; metric projection
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