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- W71073349 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 ε X and W is a closed downward subset of X." @default.
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- W71073349 date "2006-03-01" @default.
- W71073349 modified "2023-09-30" @default.
- W71073349 title "Best approximation by downward sets with applications" @default.
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- W71073349 doi "https://doi.org/10.1007/bf03218696" @default.
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