Weak convergence theorems for nonexpansive mappings and monotone mappings (Q1422867)

Let \(K\) be a closed convex subset of a real Hilbert space \(H\), \(A:K\rightarrow H\) be inverse strongly monotone, and \(S:K\rightarrow K\) be nonexpansive. Assuming that the set of solutions of the variational inequality for \(A\) and the set of fixed points of \(S\) have a nonempty intersection, the authors introduce an iteration process that is shown to generate a sequence converging weakly to an element of this intersection. This is the main result of the paper, which is then applied to obtain a sequence converging to a common fixed point of a nonexpansive map and a strictly pseudocontractive map.