Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces

Let H be a Hilbert space and C a nonempty closed convex subset of H. Let A : C → H be a maximal monotone mapping and f : C → C a bounded demicontinuous strong pseudocontraction. Let {xt} be the unique solution to the equation f x x tAx. Then{xt} is bounded if and only if {xt} converges strongly to a zero point of A as t → ∞ which is the unique solution in A−1 0 , where A−1 0 denotes the zero set of A, to the following variational inequality 〈f p − p, y − p〉 ≤ 0, for all y ∈ A−1 0 .