International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3103-3110
doi:10.1155/IJMMS.2005.3103
Implicit iteration process of nonexpansive non-self-mappings
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 14 February 2005; Revised 14 June 2005
Copyright © 2005 Somyot Plubtieng and Rattanaporn Punpaeng. 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
Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(1−βn)yn+βnPTyn], and zn=P[(1−αn)u+αnTP[(1−βn)zn+βnTzn]], where {αn}⊆(0,1), 0≤βn≤β<1 and αn→1 as n→∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others.