Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 745010, 7 pages
doi:10.1155/2008/745010
Research Article

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Satit Saejung

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received 28 November 2007; Revised 15 January 2008; Accepted 30 January 2008

Academic Editor: William A. Kirk

Copyright © 2008 Satit Saejung. 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 prove a convergence theorem by the new iterative method introduced by Takahashi et al. (2007). Our result does not use Bochner integrals so it is different from that by Takahashi et al. We also correct the strong convergence theorem recently proved by He and Chen (2007).