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The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces

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  • XianFa Luo
  • JianYong Wang

Abstract

Let be a closed bounded convex subset of a real Banach space with as its interior and the Minkowski functional generated by the set . For a nonempty set in and , is called the generalized best approximation to from if for all . In this paper, we will give a distance formula under from a point to a closed hyperplane in determined by a nonzero continuous linear functional in and a real number α , a representation of the generalized metric projection onto , and investigate the continuity of this generalized metric projection, extending corresponding results for the case of norm.

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  • XianFa Luo & JianYong Wang, 2013. "The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, November.
    • Handle: RePEc:hin:jnlaaa:504076
    DOI: 10.1155/2013/504076
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