Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 907275, 16 pages
Research Article

Strong Convergence of a Generalized Iterative Method for Semigroups of Nonexpansive Mappings in Hilbert Spaces

Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51664, Iran

Received 20 April 2010; Accepted 18 June 2010

Academic Editor: A. T. M. Lau

Copyright © 2010 Husain Piri and Hamid Vaezi. 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.


Using δ-strongly accretive and λ-strictly pseudocontractive mapping, we introduce a general iterative method for finding a common fixed point of a semigroup of non-expansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real-valued functions of the semigroup. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality.