BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS  

作　　者：H.Mohebi A.M.Rubinov 

机构地区：[1]Shahid Bahonar University of Kerman Iran [2]University of Ballarat Australia

出　　处：《Analysis in Theory and Applications》2006年第1期20-40,共21页分析理论与应用（英文刊）

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 XWe 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

关 键 词：best approximation downward set proximinal set Chebyshev set Banach lattice 

分 类 号：O241.5[理学—计算数学]