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Bulletin of the London Mathematical Society 2006 38(6):1009-1018; doi:10.1112/S0024609306018893
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© Oxford University Press

Common Fixed Points of One-Parameter Nonexpansive Semigroups

Tomonari Suzuki

Department of Mathematics, Kyushu Institute of Technology Sensuicho, Tobata, Kitakyushu 804-8550, Japan e-mail: suzuki-t{at}mns.kyutech.ac.jp

Received 30 May 2005. Revision received 9 November 2005.

In this paper, we show that the set of all common fixed points of a one-parameter nonexpansive semigroup is that of some single nonexpansive mapping. We next compare our result with Bruck's famous fixed-point theorem. We finally prove very simple convergence theorems to a common fixed point. In our discussion, we assume neither the strict convexity of the underlying space, nor the weak compactness of the domain of a nonexpansive semigroup. 2000 Mathematics Subject Classification 47H20 (primary), 47H10 (secondary).

The author is supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.


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