Open Access

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces

Fixed Point Theory and Applications20052005:906783

DOI: 10.1155/FPTA.2005.343

Received: 24 February 2005

Published: 25 October 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.

Authors’ Affiliations

(1)
Department of Mathematics, Shibaura Institute of Technology
(2)
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology

Copyright

© Atsushiba and Takahashi 2005