On the Smoothness of the Metric Projection and Its Application to Proximinality in Lp(S, X) Original Research Article

We obtain some smoothness properties for the metric projection that hold for a large class of proximinal subspaces. As a consequence of this and various other results, we establish the proximinality of Lp(S, G) in Lp(S, X), 0 < p ≤ ∞, for a wide class of proximinal subspaces G in X. Thus generalizing many previously known results.