International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 649510, 9 pages
doi:10.1155/2008/649510
Research Article
Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Received 21 May 2008; Accepted 14 August 2008
Academic Editor: Petru Jebelean
Copyright © 2008 Lili He et al. 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
Let C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges strongly to a common fixed point of S and T. The results generalize and unify the corresponding results.