Abstract
In this paper, we affirmatively answer an open question raised by P.Szeptycki and Vlech in (9) and give a new characterization of p-uniformly convex Banach space. The Lipschitz stability of the set of ε-Chebyshev centers Gε(A) under the perturbations of A and G is also proved.
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Jia-ping, W., Xin-tai, Y. Chebyshev centers, ε-Chebyshev centers and the Hausdorff metric. Manuscripta Math 63, 115–128 (1989). https://doi.org/10.1007/BF01173706
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DOI: https://doi.org/10.1007/BF01173706