Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

Assume thatFis a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subsetCof a real Hilbert spaceH. Assume also thatΩis the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings onC. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbationF, which generates two sequences from an arbitrary initial pointx0∈H. These two sequences are shown to converge in norm to the same pointPΩx0under very mild assumptions.