On the metric projection onto a family of closed convex sets in a uniformly convex Banach space

Authors: Bùi Trọng Kiên,

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Publisher, magazine: ,

Publication year: 2002

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Abstract

From the text: Extending a result of \textit{D. N. Yen} [Appl. Math. Optimization 31, No. 3, 245–255 (1995; Zbl 0821.49011)] the author studies the behavior of the metric projection of a pseudo-Lipschitz multifunction \(K\) between metric spaces when the range is a uniformly convex Banach space. In case of \(L_p\), \(1<p \leq 2\), he obtains the result that locally \[ \|P_{K(\lambda)}(y)-P_{K(\mu)}(y)\|_p \leq M \sqrt{d(\lambda,\mu)}, \] for some constant \(M>0\).

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