Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 732872, 16 pages
doi:10.1155/2010/732872
Research Article

Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Point

Yasunori Kimura1 and Kazuhide Nakajo2

1Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
2Faculty of Engineering, Tamagawa University, Tamagawa-Gakuen, Machida-shi, Tokyo 194-8610, Japan

Received 7 October 2009; Accepted 19 October 2009

Academic Editor: Anthony To Ming Lau

Copyright © 2010 Yasunori Kimura and Kazuhide Nakajo. 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

Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space.