Copyright © 2012 O. A. Daman and H. Zegeye. 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

It is our purpose, in this paper, to prove strong convergence of Halpern-Ishikawa iteration method to a common fixed point of finite family of Lipschitz pseudocontractive mappings. There is no compactness assumption imposed either on C or on T. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.