A decomposition relative to convex sets
M. Z. Nashed · Proceedings of the American Mathematical Society · 1968
1. The purpose of this note is to prove a decomposition theorem which asserts that, given a closed convex set C in a Hilbert space H, each element uEzH can be uniquely decomposed as the sum of an element xCH and the closest-point projection of x on C. Moreover, x depends continuously on u and can be determined by an iterative procedure. We also prove a theorem on the solution by iteration of monotone operator equations.