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Closed convex sets and their best simultaneous approximation properties with applications

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Abstract

We develop a theory of best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of closed convex sets, and give necessary and sufficient conditions for the uniqueness of best simultaneous approximation. We give a characterization of simultaneous pseudo-Chebyshev and quasi-Chebyshev closed convex sets in X. Also, we present various characterizations of best simultaneous approximation of elements by closed convex sets in terms of the extremal points of the closed unit ball B X* of X*.

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Authors and Affiliations

  1. Mahani Mathematical Research Center, University of Kerman, Kerman, Iran

    H. Mohebi & E. Naraghirad

Authors
  1. H. Mohebi
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  2. E. Naraghirad
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Correspondence to H. Mohebi.

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Mohebi, H., Naraghirad, E. Closed convex sets and their best simultaneous approximation properties with applications. Optimization Letters 1, 313–328 (2007). https://doi.org/10.1007/s11590-006-0017-2

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  • DOI: https://doi.org/10.1007/s11590-006-0017-2

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