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- Title
Hybrid Method with Perturbation for Lipschitzian Pseudocontractions.
- Authors
Ceng, Lu-Chuan; Wen, Ching-Feng
- 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 є H. These two sequences are shown to converge in norm to the same point PΩx0 under very mild assumptions.
- Subjects
HYBRID systems; PERTURBATION theory; NONLINEAR operator equations; MONOTONE operators; MODULES (Algebra); ITERATIVE methods (Mathematics)
- Publication
Journal of Applied Mathematics, 2012, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2012/250538