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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The set of common fixed points of a one-parameter continuous semigroup of mappings is $F \big ( T(1) \big ) \cap F \big ( T(\sqrt 2) \big )$
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by Tomonari Suzuki PDF
Proc. Amer. Math. Soc. 134 (2006), 673-681 Request permission

Abstract:

In this paper we prove the following theorem: Let $\{ T(t) : t \geq 0 \}$ be a one-parameter continuous semigroup of mappings on a subset $C$ of a Banach space $E$. The set of all fixed points of $T(t)$ is denoted by $F \big ( T(t) \big )$ for each $t \geq 0$. Then \[ \bigcap _{t \geq 0} F \big ( T(t) \big ) = F \big ( T(1) \big ) \cap F \big ( T(\sqrt 2) \big ) \] holds. Using this theorem, we discuss convergence theorems to a common fixed point of $\{ T(t) : t \geq 0 \}$.
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Additional Information
  • Tomonari Suzuki
  • Affiliation: Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
  • Email: suzuki-t@mns.kyutech.ac.jp
  • Received by editor(s): December 17, 2003
  • Published electronically: September 28, 2005
  • Additional Notes: The author was supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 673-681
  • MSC (2000): Primary 47H20, 47H10
  • DOI: https://doi.org/10.1090/S0002-9939-05-08361-9
  • MathSciNet review: 2180883