Continuous selection from the sets of best and near-best approximation
- Autores: Tsar’kov I.1
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Afiliações:
- Mechanics and Mathematics Faculty
- Edição: Volume 96, Nº 1 (2017)
- Páginas: 362-364
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225252
- DOI: https://doi.org/10.1134/S1064562417040196
- ID: 225252
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Resumo
The paper studies approximation and structural geometric-topological properties of sets in normed and more general (asymmetric) spaces for which there exists a continuous selection for the best and near-best approximation operators. Sufficient conditions on the metric projection of sets which ensure the existence of a continuous selection for this projection are obtained, and the structural properties of such sets are determined. The existence of a continuous selection for the near-best approximation operator on a finite-dimensional space more general than a normed space is investigated. It is shown that the lower semicontinuity of the metric projection is sufficient for the existence of a continuous selection for the near-best approximation operator in the general case.
Sobre autores
I. Tsar’kov
Mechanics and Mathematics Faculty
Autor responsável pela correspondência
Email: tsar@mech.math.msu.su
Rússia, Moscow, 119991