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Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces

Fixed Point Theory and Applications20052005:906783

  • Received: 24 February 2005
  • Published:


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

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


© Atsushiba and Takahashi 2005