Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces

Abstract

Let be a Hilbert space and a nonempty closed convex subset of . Let be a maximal monotone mapping and a bounded demicontinuous strong pseudocontraction. Let be the unique solution to the equation . Then is bounded if and only if converges strongly to a zero point of A as which is the unique solution in , where denotes the zero set of , to the following variational inequality , for all .