The Representive of Metric Projection on the Linear Manifold in Arbitary Banach Space

Abstract:

      This paper established the necessary and sufficient condition for existence of (set-valued) metric projection on the linear manifold in arbitary Banach space by the normalized duality mapping. Meanwhile, a representive of metric projection on the linear manifold in arbitary Banach space was given, so was the distance formulas from a point to the linear manifold in Banach space. These indeed extended and improved the corresponding results obtained by Wang Yuwen and Yu Jinfeng under the strong assumption that the space X was a reflexive, smooth and strictly convex Banach space.