| BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS |
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| 作者姓名： | H. Mohebi A. M. Rubinov |
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| 作者单位： | [1]Shahid Bahonar University of Kerman, Iran [2]University of Ballarat, Australia |
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| 摘 要： | 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 and W is a closed downward subset of X
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| 关 键 词： | 最佳逼近 下行设置 Chebyshev设置 Banach点阵 |
| 收稿时间： | 2005-04-21 |
Best approximation by downward sets with applications |
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| H. Mohebi A. M. Rubinov.BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS[J].Analysis in Theory and Applications,2006,22(1):20-40. |
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| Authors: | H Mohebi A M Rubinov |
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| Institution: | (3) Mahani Mathematical Research Center, and Department of Mathematics, University of Kerman, Kerman, Iran; |
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| 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 ∈ X and W is a closed downward subset of X. |
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| Keywords: | best approximation downward set proximinal set Chebyshev set Banach lattice APPLICATIONS SETS APPROXIMATION results used examination prove boundary point Chebyshev characterize subsets sufficient conditions elements closed study best approximation ordered space develop theory class |
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