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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

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