Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 476913, 8 pages
doi:10.1155/2010/476913
Research Article

Viscosity Approximation to Common Fixed Points of Families of Nonexpansive Mappings with Weakly Contractive Mappings

A. Razani1,2 and S. Homaeipour1

1Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran
2School of Mathematics, Institute for Research in Fundamental Sciences, P.O. Box 19395-5746, Tehran, Iran

Received 5 June 2010; Accepted 26 July 2010

Academic Editor: Brailey Sims

Copyright © 2010 A. Razani and S. Homaeipour. 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

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence xn=λnf(xn)+(1−λn)Tnxn, where λn∈ (0, 1), {Tn} is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {xn} is proved.