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Best approximation by downward sets with applications

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Analysis in Theory and Applications

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.

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Authors and Affiliations

  1. Shadhid Bahonar University of Kerman, Kerman, Iran

    H. Mohebi

  2. University of Ballart, Victoria, Australia

    H. Mohebi & A. M. Rubinov

Authors
  1. H. Mohebi
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  2. A. M. Rubinov
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Mohebi, H., Rubinov, A.M. Best approximation by downward sets with applications. Analysis in Theory and Applications 22, 20–40 (2006). https://doi.org/10.1007/BF03218696

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  • DOI: https://doi.org/10.1007/BF03218696

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