1.Fariborz Maseeh Department of Mathematics and Statistics,Portland State University,Portland,USA;2.CCQCN, Department of Physics,University of Crete,Heraklion,Greece
Abstract:
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with (C^{1,1})boundary which possesses the same property.