# On the uniform continuity of metric projections in Banach spaces

Research paper by Xu Zongben, G. F. Roach

Indexed on: 01 Sep '92Published on: 01 Sep '92Published in: Approximation Theory and its Applications

#### Abstract

Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space. It is proved that the metric projection PM of X onto M is uniformly continuous on every bounded subset of X. Moreover, a global and explicit estimate on the modulus of continuity of the metric projection is obtained.