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Open Access

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces

Fixed Point Theory and Applications20052005:906783

https://doi.org/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, Saitama-City, Japan
(2)
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan

Copyright

© Atsushiba and Takahashi 2005