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This article is cited in 17 scientific papers (total in 17 papers)
Properties of the metric projection on weakly vial-convex sets and parametrization of set-valued mappings with weakly convex images
M. V. Balashov, G. E. Ivanov Moscow Institute of Physics and Technology
Abstract:
We continue studying the class of weakly convex sets (in the sense of Vial). For points in a sufficiently small neighborhood of a closed weakly convex subset in Hilbert space, we prove that the metric projection on this set exists and is unique. In other words, we show that the closed weakly convex sets have a Chebyshev layer. We prove that the metric projection of a point on a weakly convex set satisfies the Lipschitz condition with respect to a point and the Hölder condition with exponent $1/2$ with respect to a set. We develop a method for constructing a continuous parametrization of a set-valued mapping with weakly convex images. We obtain an explicit estimate for the modulus of continuity of the parametrizing function.
Received: 14.03.2005
Citation:
M. V. Balashov, G. E. Ivanov, “Properties of the metric projection on weakly vial-convex sets and parametrization of set-valued mappings with weakly convex images”, Mat. Zametki, 80:4 (2006), 483–489; Math. Notes, 80:4 (2006), 461–467
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https://www.mathnet.ru/eng/mzm2840https://doi.org/10.4213/mzm2840 https://www.mathnet.ru/eng/mzm/v80/i4/p483
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Abstract page: | 608 | Full-text PDF : | 329 | References: | 63 | First page: | 2 |
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