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Random fixed point results for Suzuki type random operators and applications. (English) Zbl 1296.60176

Summary: In aim of this paper is to prove the random version of Suzuki fixed point theorem in a separable metric space. Our main result generalizes the results of A. T. Bharucha-Reid [Bull. Am. Math. Soc. 82, 641–657 (1976; Zbl 0339.60061)] and T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)]. Moreover, we show that these maps satisfy property P. Application to a certain class of random functional equations arising in dynamical programming is also obtained.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
54H25 Fixed-point and coincidence theorems (topological aspects)
41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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