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

 

A random fixed point theorem for multivalued nonexpansive operators in uniformly convex Banach spaces


Author: Hong Kun Xu
Journal: Proc. Amer. Math. Soc. 117 (1993), 1089-1092
MSC: Primary 47H40; Secondary 47H09, 47H10, 60H25
MathSciNet review: 1123670
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Abstract: Let $ (\Omega ,\Sigma )$ be a measurable space with $ \Sigma $ a sigma-algebra of subsets of $ \Omega $, and let $ C$ be a nonempty, bounded, closed, convex, and separable subset of a uniformly convex Banach space $ X$. It is shown that every multivalued nonexpansive random operator $ T:\Omega \times C \to K(C)$ has a random fixed point, where $ K(C)$ is the family of all nonempty compact subsets of $ C$ endowed with the Hausdorff metric induced by the norm of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1123670-8
PII: S 0002-9939(1993)1123670-8
Keywords: Random fixed point, multivalued nonexpansive operator, uniformly convex Banach space
Article copyright: © Copyright 1993 American Mathematical Society