Uniform Lipschitz Continuity of Best l -Approximations by Polyhedral Sets

In this paper we prove that the metric projection PK, p onto a polyhedral subset K of Rn, endowed with the p-norm, is uniformly Lipschitz continuous with respect to p, 1-p-`. As a consequence the strict best approximation and the natural best approximation are Lipschitz continuous selections for the metric projections PK, ` and PK, 1, respectively. This extends a recent analogous result in Berens et al. w J. Math. Anal. Appl. 213 1997., 183]201x on linear subspaces