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Convergence of almost-orbits of nonexpansive semigroups in Banach spaces
Author(s):
Anthony
To-Ming
Lau;
Koji
Nishiura;
Wataru
Takahashi
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3143-3150.
MSC (2000):
Primary 47H20;
Secondary 47H09
Posted:
June 19, 2007
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Abstract:
The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.
References:
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Additional Information:
Anthony
To-Ming
Lau
Affiliation:
Department of Mathematical and Satistical Sciences, University of Albert, Edmonton, Alberta, Canada T6G 2G1
Email:
tlau@math.ualberta.ca
Koji
Nishiura
Affiliation:
Department of General Education, Fukushima National College of Technology, Taira, Iwaki-shi 970-8034, Japan
Email:
nishiura@fukushima-nct.ac.jp
Wataru
Takahashi
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
Email:
wataru@is.titech.ac.jp
DOI:
10.1090/S0002-9939-07-08999-X
PII:
S 0002-9939(07)08999-X
Keywords:
Mean ergodic theorem,
nonexpansive semigroup,
almost-orbit,
regular net,
invariant mean
Received by editor(s):
March 31, 2006
Posted:
June 19, 2007
Additional Notes:
This research was supported by NSERC grant A-7679 and by Grant-in-Aid for General Scientific Research No. 15540157, the Ministry of Education, Science, Sports and Culture, Japan
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2007,
American Mathematical Society
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