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On deterministic and random fixed points. (English) Zbl 0801.47044
Summary: 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.

MSC:
47H10 Fixed-point theorems
60H25 Random operators and equations (aspects of stochastic analysis)
47H40 Random nonlinear operators
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