Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: Tomonari Suzuki
Journal: Proc. Amer. Math. Soc. 134 (2006), 673-681
MSC (2000): Primary 47H20, 47H10
Published electronically: September 28, 2005
MathSciNet review: 2180883
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

$\displaystyle \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 \}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H20, 47H10

Retrieve articles in all journals with MSC (2000): 47H20, 47H10


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

DOI: http://dx.doi.org/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
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.