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2012 Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
Lu-Chuan Ceng, Ching-Feng Wen
J. Appl. Math. 2012(SI15): 1-20 (2012). DOI: 10.1155/2012/250538


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 x0H. These two sequences are shown to converge in norm to the same point Px0 under very mild assumptions.


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Lu-Chuan Ceng. Ching-Feng Wen. "Hybrid Method with Perturbation for Lipschitzian Pseudocontractions." J. Appl. Math. 2012 (SI15) 1 - 20, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.65082
MathSciNet: MR2948159
Digital Object Identifier: 10.1155/2012/250538

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI15 • 2012
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