Let D be a closed convex subset of

Let D be a closed convex subset of H . For every x∈H, there exists a unique nearest point in D denoted by PDx, that is, ‖x-PDx‖⩽‖x-y‖ for every y∈D. This mapping PD is called the metric projection of H onto D . It is known that PD is firmly nonexpansive, that is, the following hold: