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2014 The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces
Zihou Zhang, Chunyan Liu
Abstr. Appl. Anal. 2014: 1-5 (2014). DOI: 10.1155/2014/908676

Abstract

We show a necessary and sufficient condition for the existence of metric projection on a class of half-space Kx0*,c={xX: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.

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Zihou Zhang. Chunyan Liu. "The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/908676

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023289
MathSciNet: MR3173296
Digital Object Identifier: 10.1155/2014/908676

Rights: Copyright © 2014 Hindawi

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