Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 484061, 17 pages
http://dx.doi.org/10.5402/2011/484061
Research Article

A Viscosity Approximation Method with a Weakly Contractive Mapping of General Iterative Processes for Nonexpansive Semigroups in Banach Spaces

1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng Saen Campus, Nakhonpathom 73140, Thailand

Received 21 April 2011; Accepted 9 June 2011

Academic Editor: R. Couturier

Copyright Β© 2011 Pongsakorn Sunthrayuth 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 introduce a new viscosity approximation method with a weakly contractive mapping of general iterative processes for finding common fixed point of nonexpansive semigroups {𝑇(𝑑)βˆΆπ‘‘βˆˆβ„+} in the framework of Banach spaces. We proved that under some mild conditions these iterative processes converge strongly to the common fixed point of {𝑇(𝑑)βˆΆπ‘‘βˆˆβ„+}, which is the unique solution of some variational inequality. The results obtained in this paper extend and improve on the recent results of Li et al. (2009), Chen and He (2007), and many others as special cases.