Fixed Point Theory and Applications
Volume 2005 (2005), Issue 3, Pages 343-354

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces

Sachiko Atsushiba1 and Wataru Takahashi2

1Department of Mathematics, Shibaura Institute of Technology, Fukasaku, Minuma-ku, Saitama-City, Saitama 337-8570, Japan
2Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan

Received 24 February 2005

Copyright © 2005 Sachiko Atsushiba and Wataru Takahashi. 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.


We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.