... and 0 <η1≤ αn,j1≤ θ1< 1 for all n ∈ N, for all j 1, 2, ,N− 1, 0 <ηN≤αn,N1≤ 1 and 0 ≤ αn,j2,αn,j3≤ θ3< 1 for all n ∈ N, for all j 1, 2, ,N.Let{xn}, {un}, ... αn,j3|→0 as n →∞, for all j ∈{1, 2, 3, ,N}.Then the sequence {xn}, {yn}, {un} converges strongly to z PFfz, and z is solution ofAx∗,x− x∗≥ 0. 4.5Proof. For every i ∈{1, ... lemmas that will be used for our main resultin the next section.Let C be closed convex subset of a real Hilbert space H,andletPCbe the metricprojection of H onto C,thatis,forx ∈ H, PCx satisfies...