Journal of Applied Mathematics
Volume 2012 (2012), Article ID 250538, 20 pages
http://dx.doi.org/10.1155/2012/250538
Research Article

Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

Lu-Chuan Ceng1 and Ching-Feng Wen2

1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan

Received 21 May 2012; Accepted 5 June 2012

Academic Editor: Jen-Chih Yao

Copyright © 2012 Lu-Chuan Ceng and Ching-Feng Wen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 𝑥 0 ∈ 𝐻 . These two sequences are shown to converge in norm to the same point 𝑃 Ω 𝑥 0 under very mild assumptions.