5. The Problem of Proximinality
E. Ward Cheney · Society for Industrial and Applied Mathematics eBooks · 1986
A subspace U in a Banach space X is said to be proximinal if each x ∈ X possesses at least one best approximation in U. If U is proximinal, then there exists a map A : X → U, called a proximity map, such that‖x−Ax‖=dist(x,U).One must expect in general that A will be nonlinear and discontinuous.