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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On deterministic and random fixed points


Authors: Kok-Keong Tan and Xian-Zhi Yuan
Journal: Proc. Amer. Math. Soc. 119 (1993), 849-856
MSC: Primary 47H10; Secondary 47H40, 60B99, 60H25
MathSciNet review: 1169051
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Abstract: Based on an extension of Aumann's measurable selection theorem due to Leese, it is shown that each fixed point theorem for $ F(\omega , \cdot )$ produces a random fixed point theorem for $ F$ provided the $ \sigma $-algebra $ \Sigma $ for $ \Omega $ is a Suslin family and $ F$ has a measurable graph (in particular, when $ F$ is random continuous with closed values and $ X$ is a separable metric space). As applications and illustrations, some random fixed points in the literature are obtained or extended.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1169051-2
PII: S 0002-9939(1993)1169051-2
Keywords: Fixed point theorem, deterministic fixed point, random fixed point theorem, measurable space, Suslin space, Suslin family, measurable selection theorem
Article copyright: © Copyright 1993 American Mathematical Society