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