Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

Lu-Chuan Ceng and Ching-Feng Wen

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
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https://doi.org/10.1155/2012/250538

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:250538

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