Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 149483, 11 pages
Research Article

Strong Convergence of Viscosity Methods for Continuous Pseudocontractions in Banach Spaces

Filomena Cianciaruso,1 Giuseppe Marino,1 Luigi Muglia,1 and Haiyun Zhou2

1Dipartimento di Matematica, Universitá della Calabria, Campus di Arcavacata, Arcavacata di Rende, 87036 Rende, Italy
2Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 13 July 2008; Accepted 15 October 2008

Academic Editor: Hong Kun Xu

Copyright © 2008 Filomena Cianciaruso 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.


We define a viscosity method for continuous pseudocontractive mappings defined on closed and convex subsets of reflexive Banach spaces with a uniformly Gâteaux differentiable norm. We prove the convergence of these schemes improving the main theorems in the work by Y. Yao et al. (2007) and H. Zhou (2008).