2015
DOI: 10.1007/s11228-015-0350-7
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On Closures of Preimages of Metric Projection Mappings in Hilbert Spaces

Abstract: The closure of preimages (inverse images) of metric projection mappings to a given set in a Hilbert space are investigated. In particular, some properties of fibers over singletons (level sets or preimages of singletons) of the metric projection are provided. One of them, a sufficient condition for the convergence of minimizing sequence for a giving point, ensures the convergence of a subsequence of minimizing points, thus the limit of the subsequence belongs to the image of the metric projection. Several exam… Show more

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“…It is valuable to have results preserving a relative compactness of the sequence, see, for example, Proposition 3.1 in [14]. Below a result of this kind is presented in the Hilbert space setting.…”
Section: Preliminariesmentioning
confidence: 99%
“…It is valuable to have results preserving a relative compactness of the sequence, see, for example, Proposition 3.1 in [14]. Below a result of this kind is presented in the Hilbert space setting.…”
Section: Preliminariesmentioning
confidence: 99%