Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 509-521
doi:10.1155/JIA.2005.509
Abstract
We prove that the projection operator on a nonempty closed convex subset C of a uniformly convex Banach spaces is uniformly
continuous on bounded sets and we provide an estimate of its
modulus of uniform continuity. We derive this result from a study
of the dependence of the projection on C of a given point when
C varies.