International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 48648, 10 pages
Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 26 October 2006; Revised 22 January 2007; Accepted 28 January 2007
Academic Editor: Andrei I. Volodin
Copyright © 2007 Rabian Wangkeeree. 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.
Viscosity approximation methods for nonexpansive nonself-mappings are studied.
Let be a nonempty closed convex subset of Hilbert space , a metric projection of onto and let be a nonexpansive nonself-mapping from into . For a contraction on and , let be the unique fixed point of the contraction . Consider also the iterative processes
and generated by , and where is a real sequence in an interval . Strong convergence of the sequences , and to a fixed point of which solves some variational inequalities is obtained under certain appropriate conditions on the real sequences and .