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 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 . These two sequences are shown to converge in norm to the same point under very mild assumptions.
Lu-Chuan Ceng. Ching-Feng Wen. "Hybrid Method with Perturbation for Lipschitzian Pseudocontractions." J. Appl. Math. 2012 (SI15) 1 - 20, 2012. https://doi.org/10.1155/2012/250538