Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

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 hybri...

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Bibliographic Details
Main Authors: Lu-Chuan Ceng, Ching-Feng Wen
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/250538
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Summary: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.
ISSN:1110-757X
1687-0042