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Abstract and Applied Analysis
Volume 2014, Article ID 908676, 5 pages
Research Article

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

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China

Received 20 October 2013; Accepted 31 December 2013; Published 17 February 2014

Academic Editor: Khalil Ezzinbi

Copyright © 2014 Zihou Zhang and Chunyan Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.