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Random fixed points of set-valued operators
Author(s):
Tomás
Domínguez
Benavides;
Genaro
López
Acedo;
Hong-Kun
Xu
Journal:
Proc. Amer. Math. Soc.
124
(1996),
831-838.
MSC (1991):
Primary 47H10, 47H40;
Secondary 47H09, 60H25
MathSciNet review:
1301487
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Abstract:
Some random fixed point theorems for set-valued operators are obtained. The measurability of certain marginal maps is also studied. The underlying measurable space is not assumed to be a Suslin family.
References:
- 1.
- J.-P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser, Boston, (1990) MR 91d:49001
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- ------, A random fixed point theorem for multivalued nonexpansive operators in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 117 (1993), 1089--1092. MR 93e:47092
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Additional Information:
Tomás
Domínguez
Benavides
Affiliation:
Departmento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
Genaro
López
Acedo
Affiliation:
Departmento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
Email:
ayerbe@cica.es
Hong-Kun
Xu
Affiliation:
Institute of Applied Mathematics, East China University of Science and Technology, Shanghai 200237, China
Address at time of publication:
Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa
Email:
hkxu@pixie.udw.ac.za
DOI:
10.1090/S0002-9939-96-03062-6
PII:
S 0002-9939(96)03062-6
Keywords:
Random fixed point,
set-valued operator,
measurable space,
Hausdorff distance,
measurable selection,
nonexpansive operator,
condensing operator,
marginal map
Received by editor(s):
July 29, 1993
Received by editor(s) in revised form:
September 12, 1994
Additional Notes:
The first and second authors' research was partially supported by DGICYT under project PB 90-0903 and the Junta de Andalucia
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
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