Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
Lu-Chuan Ceng, Ching‐Feng Wen · Journal of Applied Mathematics · 2012
Assume that F is a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subset C of a real Hilbert space H. Assume also that Ω 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.