Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

Assume that F is a nonlinear operator which is Lipschitzian and stronglymonotone on a nonempty closed convex subset C of a real Hilbert space H. Assume also thatΩ is the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings on C. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbation F, which generates two sequences from an arbitrary initial point x0 ∈ H. These two sequences are shown to converge in norm to the same point PΩx0 under very mild assumptions.