Proceedings of the American Mathematical Society

The set of common fixed points of a one-parameter continuous semigroup of mappings is $F \big( T(1) \big) \cap F \big( T(\sqrt2) \big)$

Author(s): Tomonari Suzuki
Journal: Proc. Amer. Math. Soc. 134 (2006), 673-681.
MSC (2000): Primary 47H20, 47H10
Posted: September 28, 2005
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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

of a Banach space

. The set of all fixed points of

is denoted by $F \big( T(t) \big)$ for each $t \geq 0$ . Then

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Tomonari Suzuki
Affiliation: Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
Email: suzuki-t@mns.kyutech.ac.jp

DOI: 10.1090/S0002-9939-05-08361-9
PII: S 0002-9939(05)08361-9
Keywords: Nonexpansive semigroup, common fixed point, irrational number
Received by editor(s): December 17, 2003
Posted: 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 of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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