Journal of Applied Mathematics
Volume 2012 (2012), Article ID 506976, 14 pages
http://dx.doi.org/10.1155/2012/506976
Research Article

A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

Kamonrat Nammanee,1 Suthep Suantai,2,3 and Prasit Cholamjiak1,3

1School of Science, University of Phayao, Phayao 56000, Thailand
2Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 23 November 2011; Accepted 27 January 2012

Academic Editor: Giuseppe Marino

Copyright © 2012 Kamonrat Nammanee 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

We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞). Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.