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.
"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