Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 3, Pages 343-354
doi:10.1155/FPTA.2005.343

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

Abstract

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.