A bound for the modulus of continuity for metric projections in a uniformly convex and uniformly smooth Banach space

In 1979, Bjornestal obtained a local estimate for a modulus of uniform continuity of the metric projection operator on a closed subspace in a uniformly convex and uniformly smooth Banach space B. In the present paper we give the global version of this result for the projection operator on an arbitrary closed convex set in B. (C) 1996 Academic Press, Inc.