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COMMON FIXED POINTS OF ONE-PARAMETER NONEXPANSIVE SEMIGROUPS

Published online by Cambridge University Press:  19 December 2006

TOMONARI SUZUKI
TOMONARI SUZUKI
Affiliation:
Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japansuzuki-t@mns.kyutech.ac.jp
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Abstract

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.

Keywords

47H20 (primary)47H10 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 1009 - 1018
Copyright
The London Mathematical Society 2006

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