Abstract and Applied Analysis
Volume 2009 (2009), Article ID 297565, 16 pages
doi:10.1155/2009/297565
Research Article

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

Watcharaporn Cholamjiak1,2 and Suthep Suantai1,2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2PERDO National Centre of Excellence in Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 24 August 2009; Revised 5 November 2009; Accepted 27 November 2009

Academic Editor: Simeon Reich

Copyright © 2009 Watcharaporn Cholamjiak and Suthep Suantai. 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

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).