- Title
- Best approximation by downward sets with applications
- Creator
- Rubinov, Alex; Mohebi, Hossein
- Date
- 2006
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/67598
- Identifier
- vital:760
- Identifier
- ISSN:1672-4070
- Abstract
- We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.; C1
- Publisher
- The Netherlands Springer
- Relation
- Analysis in Theory and Applications Vol. 22, no. 1 (2006), p. 20-40
- Rights
- Open Access
- Rights
- Copyright Springer
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Downward sets
- Full Text
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