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

Zihou Zhang and Chunyan Liu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We show a necessary and sufficient condition for the existence of metric projection on a class of half‐space Kx0*,c={x∈X:x*(x)≤c} in Banach space. Two representations of metric projections PKx0*,c and PKx0,c are given, respectively, where Kx0,c stands for dual half‐space of Kx0*,c in dual space X*. By these representations, a series of continuity results of the metric projections PKx0*,c and PKx0,c are given. We also provide the characterization that a metric projection is a linear bounded operator.

Date: 2014
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https://doi.org/10.1155/2014/908676

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:908676

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