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The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces

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  • Zihou Zhang
  • Chunyan Liu

Abstract

We show a necessary and sufficient condition for the existence of metric projection on a class of half-space in Banach space. Two representations of metric projections and are given, respectively, where stands for dual half-space of in dual space . By these representations, a series of continuity results of the metric projections and are given. We also provide the characterization that a metric projection is a linear bounded operator.

Suggested Citation

  • Zihou Zhang & Chunyan Liu, 2014. "The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, February.
    • Handle: RePEc:hin:jnlaaa:908676
    DOI: 10.1155/2014/908676
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