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Random fixed points and random differential inclusions. (English) Zbl 0658.60090

Using the fixed point method the author studies random best approximations to random sets. The stochastic analogues of deterministic results of F. Browder and W. Petryshyn [J. Math. Anal. Appl. 20, 197-228 (1967; Zbl 0153.457)], K. Fan [Math. Z. 112, 234-240 (1969; Zbl 0185.395)] and S. Reich [J. Math. Anal. Appl. 62, 104- 113 (1978; Zbl 0375.47031)] are obtained. Two fixed point theorems for random multifunctions with stochastic domain are proved and some existence results for random differential inclusions are given.
Reviewer: O.Hadžić

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
47H10 Fixed-point theorems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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