Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

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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Main Authors: Lu-Chuan Ceng, Ching-Feng Wen
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/250538
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spelling doaj-319e60ad22b04a98b3293d32666967c32020-11-25T00:24:12ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/250538250538Hybrid Method with Perturbation for Lipschitzian PseudocontractionsLu-Chuan Ceng0Ching-Feng Wen1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaCenter for General Education, Kaohsiung Medical University, Kaohsiung 807, TaiwanAssume 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.http://dx.doi.org/10.1155/2012/250538
collection DOAJ
language English
format Article
sources DOAJ
author Lu-Chuan Ceng
Ching-Feng Wen
spellingShingle Lu-Chuan Ceng
Ching-Feng Wen
Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
Journal of Applied Mathematics
author_facet Lu-Chuan Ceng
Ching-Feng Wen
author_sort Lu-Chuan Ceng
title Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
title_short Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
title_full Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
title_fullStr Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
title_full_unstemmed Hybrid Method with Perturbation for Lipschitzian Pseudocontractions
title_sort hybrid method with perturbation for lipschitzian pseudocontractions
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/250538
work_keys_str_mv AT luchuanceng hybridmethodwithperturbationforlipschitzianpseudocontractions
AT chingfengwen hybridmethodwithperturbationforlipschitzianpseudocontractions
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