Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 483497, 25 pages
doi:10.1155/2009/483497
Strong convergence theorems of modified Ishikawa iterations for countable hemi-relatively nonexpansive mappings in a Banach space
Narin Petrot1
, Kriengsak Wattanawitoon2
and Poom Kumam3
1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
3Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand
Abstract
We prove some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space by using the hybrid projection methods. Moreover, we also apply our results to a class of relatively nonexpansive mappings, and hence, we immediately obtain the results announced by Qin and Su's result (2007), Nilsrakoo and Saejung's result (2008), Su et al.'s result (2008), and some known corresponding results in the literatures.