Projections onto closed convex sets in Hilbert spaces

Abstract

Let X be a real Hilbert space. We give necessary and sufficient algebraic conditions for a mapping $${F\colon X \to X}$$ with a closed image set to be the metric projection mapping onto a closed convex set. We provide examples that illustrate the necessity of each of the conditions. Our characterizations generalize several results related to projections onto closed convex sets.