Abstract
Let X be a real Hilbert space. We give necessary and sufficient algebraic conditions for a mapping \({F\colon X \to X}\) with a closed image set to be the metric projection mapping onto a closed convex set. We provide examples that illustrate the necessity of each of the conditions. Our characterizations generalize several results related to projections onto closed convex sets.
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Domokos, A., Ingram, J.M. & Marsh, M.M. Projections onto closed convex sets in Hilbert spaces. Acta Math. Hungar. 152, 114–129 (2017). https://doi.org/10.1007/s10474-017-0691-9
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DOI: https://doi.org/10.1007/s10474-017-0691-9