A random fixed point theorem for multivalued nonexpansive operators in uniformly convex Banach spaces
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- by Hong Kun Xu PDF
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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 $X$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 1089-1092
- MSC: Primary 47H40; Secondary 47H09, 47H10, 60H25
- DOI: https://doi.org/10.1090/S0002-9939-1993-1123670-8
- MathSciNet review: 1123670